Abstract

We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate η (in one dimension) faster than |η|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity.

© 2012 OSA

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).
  2. V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18(14), 627 (2004).
    [CrossRef]
  3. O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
    [CrossRef]
  4. L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11(10), 1268–1270 (1999).
    [CrossRef]
  5. I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. 19(3), 537 (2002).
    [CrossRef]
  6. F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
    [CrossRef]
  7. H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
    [CrossRef] [PubMed]
  8. M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
    [CrossRef] [PubMed]
  9. B. A. Malomed, Soliton Management in Periodic Systems (Springer, New York, 2006).
  10. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
    [CrossRef]
  11. H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046610 (2005).
    [CrossRef] [PubMed]
  12. G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
    [CrossRef]
  13. J. Garnier and F. K. Abdullaev, “Transmission of matter wave solitons through nonlinear traps and barriers,” Phys. Rev. A 74(1), 013604 (2006).
    [CrossRef]
  14. D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
    [CrossRef] [PubMed]
  15. Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31(19), 2888–2890 (2006).
    [CrossRef] [PubMed]
  16. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
    [CrossRef] [PubMed]
  17. P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
    [CrossRef]
  18. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
    [CrossRef] [PubMed]
  19. Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
    [CrossRef] [PubMed]
  20. F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
    [CrossRef]
  21. H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
    [CrossRef]
  22. H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
    [CrossRef]
  23. V. Pérez-García and R. Pardo, “Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates,” Physica D 238(15), 1352–1361 (2009).
    [CrossRef]
  24. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
    [CrossRef]
  25. D. Neshev, A. Sukhorukov, Y. Kivshar, E. Ostrovskaya, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  26. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003).
    [CrossRef] [PubMed]
  27. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12(13), 2831–2837 (2004).
    [CrossRef] [PubMed]
  28. Y. J. He and H. Z. Wang, “(1+1)-dimensional dipole solitons supported by optical lattice,” Opt. Express 14(21), 9832–9837 (2006).
    [CrossRef] [PubMed]
  29. O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
    [CrossRef] [PubMed]
  30. O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
    [CrossRef] [PubMed]
  31. Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, “Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities,” Opt. Lett. 36(23), 4587–4589 (2011).
    [CrossRef] [PubMed]
  32. W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
    [CrossRef]
  33. B. A. Malomed, “Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations,” Physica D 29(1-2), 155–172 (1987).
    [CrossRef]
  34. O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. France 49(11), 1829–1833 (1988).
    [CrossRef]
  35. W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Phys. Rev. Lett. 64(7), 749–752 (1990).
    [CrossRef] [PubMed]
  36. V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
    [CrossRef]
  37. B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,” Phys. Rev. A 42(10), 6009–6014 (1990).
    [CrossRef] [PubMed]
  38. P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
    [CrossRef]
  39. C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
    [CrossRef]
  40. D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
    [CrossRef]
  41. C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
    [CrossRef]
  42. F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
    [CrossRef] [PubMed]
  43. D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
    [CrossRef] [PubMed]
  44. D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
    [CrossRef] [PubMed]
  45. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83(4), 041806 (2011).
    [CrossRef]
  46. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Dissipative surface solitons in periodic structures,” Europhys. Lett. 91(3), 34003 (2010).
    [CrossRef]
  47. V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain,” Opt. Lett. 36(1), 85–87 (2011).
    [CrossRef] [PubMed]
  48. C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
    [CrossRef]
  49. O. V. Borovkova, V. E. Lobanov, and B. A. Malomed, “Stable nonlinear amplification of solitons without gain saturation,” Europhys. Lett.in press.
  50. J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
    [CrossRef]
  51. G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
    [CrossRef]
  52. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
    [CrossRef]
  53. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
    [CrossRef]
  54. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
    [CrossRef] [PubMed]
  55. A. Sigler and B. A. Malomed, “Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations,” Physica D 212(3-4), 305–316 (2005).
    [CrossRef]
  56. L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1566), 289–313 (1972).
    [CrossRef]
  57. N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20(10), 1733 (1977).
    [CrossRef]
  58. J. Atai and B. A. Malomed, “Exact stable pulses in asymmetric linearly coupled Ginzburg–Landau equations,” Phys. Lett. A 246(5), 412–422 (1998).
    [CrossRef]

2011

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83(4), 041806 (2011).
[CrossRef]

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain,” Opt. Lett. 36(1), 85–87 (2011).
[CrossRef] [PubMed]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, “Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities,” Opt. Lett. 36(23), 4587–4589 (2011).
[CrossRef] [PubMed]

2010

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Dissipative surface solitons in periodic structures,” Europhys. Lett. 91(3), 34003 (2010).
[CrossRef]

D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[CrossRef]

2009

V. Pérez-García and R. Pardo, “Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates,” Physica D 238(15), 1352–1361 (2009).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

2008

Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
[CrossRef] [PubMed]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
[CrossRef] [PubMed]

2007

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

2006

Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31(19), 2888–2890 (2006).
[CrossRef] [PubMed]

Y. J. He and H. Z. Wang, “(1+1)-dimensional dipole solitons supported by optical lattice,” Opt. Express 14(21), 9832–9837 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
[CrossRef]

J. Garnier and F. K. Abdullaev, “Transmission of matter wave solitons through nonlinear traps and barriers,” Phys. Rev. A 74(1), 013604 (2006).
[CrossRef]

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

2005

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

A. Sigler and B. A. Malomed, “Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations,” Physica D 212(3-4), 305–316 (2005).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046610 (2005).
[CrossRef] [PubMed]

2004

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18(14), 627 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12(13), 2831–2837 (2004).
[CrossRef] [PubMed]

2003

D. Neshev, A. Sukhorukov, Y. Kivshar, E. Ostrovskaya, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003).
[CrossRef] [PubMed]

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef] [PubMed]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
[CrossRef]

2002

I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. 19(3), 537 (2002).
[CrossRef]

1999

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11(10), 1268–1270 (1999).
[CrossRef]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

1998

J. Atai and B. A. Malomed, “Exact stable pulses in asymmetric linearly coupled Ginzburg–Landau equations,” Phys. Lett. A 246(5), 412–422 (1998).
[CrossRef]

1997

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

1994

P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
[CrossRef]

1990

W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Phys. Rev. Lett. 64(7), 749–752 (1990).
[CrossRef] [PubMed]

V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
[CrossRef]

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,” Phys. Rev. A 42(10), 6009–6014 (1990).
[CrossRef] [PubMed]

1988

O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. France 49(11), 1829–1833 (1988).
[CrossRef]

1987

B. A. Malomed, “Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations,” Physica D 29(1-2), 155–172 (1987).
[CrossRef]

1977

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20(10), 1733 (1977).
[CrossRef]

1972

L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1566), 289–313 (1972).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

J. Garnier and F. K. Abdullaev, “Transmission of matter wave solitons through nonlinear traps and barriers,” Phys. Rev. A 74(1), 013604 (2006).
[CrossRef]

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

Albiez, M.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Alfimov, G. L.

D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
[CrossRef]

D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
[CrossRef] [PubMed]

Assanto, G.

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

Atai, J.

J. Atai and B. A. Malomed, “Exact stable pulses in asymmetric linearly coupled Ginzburg–Landau equations,” Phys. Lett. A 246(5), 412–422 (1998).
[CrossRef]

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
[CrossRef]

Belic, M.

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

Bishop, A. R.

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Borovkova, O. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, V. E. Lobanov, and B. A. Malomed, “Stable nonlinear amplification of solitons without gain saturation,” Europhys. Lett.in press.

Brazhnyi, V. A.

H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18(14), 627 (2004).
[CrossRef]

Caputo, J. G.

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Centurion, M.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

Chate, H.

P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
[CrossRef]

Chow, K. W.

C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

Conte, R.

P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
[CrossRef]

Corney, J.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

Cristiani, M.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Cruz, H. A.

H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
[CrossRef]

Fantoni, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

Fauve, S.

O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. France 49(11), 1829–1833 (1988).
[CrossRef]

Fibich, G.

Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
[CrossRef]

Fölling, J.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Foreman, E. A.

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Gammal, A.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

Garnier, J.

J. Garnier and F. K. Abdullaev, “Transmission of matter wave solitons through nonlinear traps and barriers,” Phys. Rev. A 74(1), 013604 (2006).
[CrossRef]

Gati, R.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Giovanazzi, S.

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

Hakim, V.

V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
[CrossRef]

He, Y. J.

Hizanidis, K.

Hocking, L. M.

L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1566), 289–313 (1972).
[CrossRef]

Hohenberg, P. C.

W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Phys. Rev. Lett. 64(7), 749–752 (1990).
[CrossRef] [PubMed]

Hoq, Q. E.

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Huang, T.

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

Hukriede, J.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
[CrossRef]

Hunsmann, S.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Ilan, B.

Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
[CrossRef] [PubMed]

Jakobsen, P.

V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
[CrossRef]

Kartashov, Y. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, “Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities,” Opt. Lett. 36(23), 4587–4589 (2011).
[CrossRef] [PubMed]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83(4), 041806 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
[CrossRef] [PubMed]

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain,” Opt. Lett. 36(1), 85–87 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Dissipative surface solitons in periodic structures,” Europhys. Lett. 91(3), 34003 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12(13), 2831–2837 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

Kip, D.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
[CrossRef]

Kivshar, Y.

Kominis, Y.

Konotop, V. V.

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83(4), 041806 (2011).
[CrossRef]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Dissipative surface solitons in periodic structures,” Europhys. Lett. 91(3), 34003 (2010).
[CrossRef]

D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
[CrossRef] [PubMed]

D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
[CrossRef]

H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18(14), 627 (2004).
[CrossRef]

Kraenkel, R. A.

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

Krolikowski, W.

Lam, C. K.

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

Lam, C.-K.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

Lobanov, V. E.

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain,” Opt. Lett. 36(1), 85–87 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, V. E. Lobanov, and B. A. Malomed, “Stable nonlinear amplification of solitons without gain saturation,” Europhys. Lett.in press.

Machacek, D. L.

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Malomed, B. A.

Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, “Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities,” Opt. Lett. 36(23), 4587–4589 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
[CrossRef] [PubMed]

C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
[CrossRef] [PubMed]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046610 (2005).
[CrossRef] [PubMed]

A. Sigler and B. A. Malomed, “Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations,” Physica D 212(3-4), 305–316 (2005).
[CrossRef]

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
[CrossRef]

I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. 19(3), 537 (2002).
[CrossRef]

J. Atai and B. A. Malomed, “Exact stable pulses in asymmetric linearly coupled Ginzburg–Landau equations,” Phys. Lett. A 246(5), 412–422 (1998).
[CrossRef]

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,” Phys. Rev. A 42(10), 6009–6014 (1990).
[CrossRef] [PubMed]

B. A. Malomed, “Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations,” Physica D 29(1-2), 155–172 (1987).
[CrossRef]

O. V. Borovkova, V. E. Lobanov, and B. A. Malomed, “Stable nonlinear amplification of solitons without gain saturation,” Europhys. Lett.in press.

Marcq, P.

P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
[CrossRef]

Milburn, G. J.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

Morsch, O.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Musslimani, Z. H.

Nepomnyashchy, A. A.

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,” Phys. Rev. A 42(10), 6009–6014 (1990).
[CrossRef] [PubMed]

Neshev, D.

Niarchou, P.

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

Oberthaler, M.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Oberthaler, M. K.

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

Ostrovskaya, E.

Pardo, R.

V. Pérez-García and R. Pardo, “Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates,” Physica D 238(15), 1352–1361 (2009).
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N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20(10), 1733 (1977).
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Pérez-García, V.

V. Pérez-García and R. Pardo, “Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates,” Physica D 238(15), 1352–1361 (2009).
[CrossRef]

Pérez-García, V. M.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

Pomeau, Y.

V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
[CrossRef]

Porter, M. A.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

Psaltis, D.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

Raghavan, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

Runde, D.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
[CrossRef]

Saito, H.

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef] [PubMed]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046610 (2005).
[CrossRef] [PubMed]

Salerno, M.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
[CrossRef]

Saxena, A.

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Schmelcher, P.

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

Shenoy, S. R.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

Sigler, A.

A. Sigler and B. A. Malomed, “Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations,” Physica D 212(3-4), 305–316 (2005).
[CrossRef]

Sivan, Y.

Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
[CrossRef]

Smerzi, A.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

Stenflo, L.

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20(10), 1733 (1977).
[CrossRef]

Stewartson, K.

L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1566), 289–313 (1972).
[CrossRef]

Sukhorukov, A.

Theocharis, G.

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

Thual, O.

O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. France 49(11), 1829–1833 (1988).
[CrossRef]

Tomio, L.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

Torner, L.

Torres, P. J.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

Towers, I.

I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. 19(3), 537 (2002).
[CrossRef]

Tsang, C. H.

C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

Ueda, M.

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef] [PubMed]

van Saarloos, W.

W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Phys. Rev. Lett. 64(7), 749–752 (1990).
[CrossRef] [PubMed]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wai, P. K. A.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

Walls, D. F.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

Wang, H. Z.

Weinstein, M. I.

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
[CrossRef]

Wright, E. M.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

Yang, J.

Yulin, A. V.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

Zezyulin, D. A.

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
[CrossRef]

D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
[CrossRef] [PubMed]

Zhong, W.-P.

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

Eur. Phys. J. D

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, “Solitons pinned to hot spots,” Eur. Phys. J. D 59(1), 81–89 (2010).
[CrossRef]

Eur. Phys. J. Spec. Top.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, “Spatial solitons supported by localized gain in nonlinear optical waveguides,” Eur. Phys. J. Spec. Top. 173(1), 233–243 (2009).
[CrossRef]

Europhys. Lett.

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Dissipative surface solitons in periodic structures,” Europhys. Lett. 91(3), 34003 (2010).
[CrossRef]

V. Hakim, P. Jakobsen, and Y. Pomeau, “Fronts vs solitary waves in non equilibrium systems,” Europhys. Lett. 11(1), 19–24 (1990).
[CrossRef]

O. V. Borovkova, V. E. Lobanov, and B. A. Malomed, “Stable nonlinear amplification of solitons without gain saturation,” Europhys. Lett.in press.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63(5), 642–648 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11(10), 1268–1270 (1999).
[CrossRef]

J. Opt. Soc. Am.

I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. 19(3), 537 (2002).
[CrossRef]

J. Phys. B

H. A. Cruz, V. A. Brazhnyi, and V. V. Konotop, “Partial delocalization of two-component condensates in optical lattices,” J. Phys. B 41(3), 035304 (2008).
[CrossRef]

J. Phys. D Appl. Phys.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36(3), R1–R16 (2003).
[CrossRef]

J. Phys. France

O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. France 49(11), 1829–1833 (1988).
[CrossRef]

Mod. Phys. Lett. B

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18(14), 627 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
[CrossRef] [PubMed]

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain,” Opt. Lett. 36(1), 85–87 (2011).
[CrossRef] [PubMed]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, “Algebraic bright and vortex solitons in defocusing media,” Opt. Lett. 36(16), 3088–3090 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, “Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities,” Opt. Lett. 36(23), 4587–4589 (2011).
[CrossRef] [PubMed]

Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31(19), 2888–2890 (2006).
[CrossRef] [PubMed]

D. Neshev, A. Sukhorukov, Y. Kivshar, E. Ostrovskaya, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003).
[CrossRef] [PubMed]

Phys. Fluids

N. R. Pereira and L. Stenflo, “Nonlinear Schrödinger equation including growth and damping,” Phys. Fluids 20(10), 1733 (1977).
[CrossRef]

Phys. Lett. A

J. Atai and B. A. Malomed, “Exact stable pulses in asymmetric linearly coupled Ginzburg–Landau equations,” Phys. Lett. A 246(5), 412–422 (1998).
[CrossRef]

Phys. Rev. A

D. A. Zezyulin, G. L. Alfimov, and V. V. Konotop, “Nonlinear modes in a complex parabolic potential,” Phys. Rev. A 81(1), 013606 (2010).
[CrossRef]

P. Niarchou, G. Theocharis, P. G. Kevrekidis, P. Schmelcher, and D. J. Frantzeskakis, “Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates,” Phys. Rev. A 76(2), 023615 (2007).
[CrossRef]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, “Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices,” Phys. Rev. A 77(2), 023615 (2008).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83(4), 041806 (2011).
[CrossRef]

F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67(1), 013605 (2003).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[CrossRef]

W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient,” Phys. Rev. A 84(4), 043801 (2011).
[CrossRef]

J. Garnier and F. K. Abdullaev, “Transmission of matter wave solitons through nonlinear traps and barriers,” Phys. Rev. A 74(1), 013604 (2006).
[CrossRef]

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,” Phys. Rev. A 42(10), 6009–6014 (1990).
[CrossRef] [PubMed]

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55(6), 4318–4324 (1997).
[CrossRef]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59(1), 620–633 (1999).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056606 (2010).
[CrossRef] [PubMed]

D. A. Zezyulin, V. V. Konotop, and G. L. Alfimov, “Dissipative double-well potential: nonlinear stationary and pulsating modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 056213 (2010).
[CrossRef] [PubMed]

C. H. Tsang, B. A. Malomed, and K. W. Chow, “Multistable dissipative structures pinned to dual hot spots,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 066609 (2011).
[CrossRef]

D. L. Machacek, E. A. Foreman, Q. E. Hoq, P. G. Kevrekidis, A. Saxena, D. J. Frantzeskakis, and A. R. Bishop, “Statics and dynamics of an inhomogeneously nonlinear lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036602 (2006).
[CrossRef] [PubMed]

Y. Sivan, G. Fibich, and B. Ilan, “Drift instability and tunneling of lattice solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(4), 045601 (2008).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046610 (2005).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, “Bright solitons from defocusing nonlinearities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3), 035602 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98(6), 064102 (2007).
[CrossRef] [PubMed]

H. Saito and M. Ueda, “Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate,” Phys. Rev. Lett. 90(4), 040403 (2003).
[CrossRef] [PubMed]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97(3), 033903 (2006).
[CrossRef] [PubMed]

W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Phys. Rev. Lett. 64(7), 749–752 (1990).
[CrossRef] [PubMed]

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction,” Phys. Rev. Lett. 95(1), 010402 (2005).
[CrossRef] [PubMed]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates,” Phys. Rev. Lett. 79(25), 4950–4953 (1997).
[CrossRef]

Physica D

A. Sigler and B. A. Malomed, “Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations,” Physica D 212(3-4), 305–316 (2005).
[CrossRef]

P. Marcq, H. Chate, and R. Conte, “Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation,” Physica D 73(4), 305–317 (1994).
[CrossRef]

G. Fibich, Y. Sivan, and M. I. Weinstein, “Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure,” Physica D 217(1), 31–57 (2006).
[CrossRef]

B. A. Malomed, “Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations,” Physica D 29(1-2), 155–172 (1987).
[CrossRef]

V. Pérez-García and R. Pardo, “Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates,” Physica D 238(15), 1352–1361 (2009).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci.

L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1566), 289–313 (1972).
[CrossRef]

Rev. Mod. Phys.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179–215 (2006).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83(1), 247–306 (2011).
[CrossRef]

Other

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

B. A. Malomed, Soliton Management in Periodic Systems (Springer, New York, 2006).

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Figures (5)

Fig. 1
Fig. 1

(Color online) Typical profiles of fundamental symmetric (a) and asymmetric (b) solitons in the focusing medium, and of the symmetric one in the defocusing medium (c) with the single-well nonlinear-absorption profile (3) [red curves for γ(η) ], at p i =1.5 , σ i =0.5 .

Fig. 2
Fig. 2

(Color online) The energy flow (a) and propagation constant (b) versus p i for symmetric (“fs”) and asymmetric (“fa”) fundamental solitons in the focusing medium with the single-well nonlinear-absorption profile (3) at σ i =0.5 . (c), (d): The same for dipole solitons in the double-well nonlinear-absorption landscape (6) at σ i =2.0 . Subscripts “fs”, “ds”, and “da” denote symmetric dipoles in the focusing and defocusing media, and asymmetric dipoles in the defocusing medium, respectively. Circles in (a),(b) correspond to the solitons in Figs. 1(a) and 1(b), while circles in (c),(d) pertain to the solitons in Figs. 4(a) and (b), respectively.

Fig. 3
Fig. 3

(Color online) Existence and stability domains in the ( σ i , p i ) plane. (a) The fundamental solitons in the focusing medium with the single-well nonlinear absorption profile (3) (the asymmetric solitons exist and are stable at p i > p i cr1 ). (b) and (c): Dipole solitons in the double-well absorption profile (6), in the focusing and defocusing media, respectively.

Fig. 4
Fig. 4

(Color online) Examples of symmetric and asymmetric dipole solitons at p i =3.0 (a) and p i =1.9 (b), respectively, in the defocusing medium with the double-well nonlinear-absorption landscape (5) [red curves for γ(η) ], at σ i =2.0 .

Fig. 5
Fig. 5

(Color online) The dynamics of dipole solitons in the focusing (a)-(c) and defocusing (d)-(f) media with the double-well nonlinear-loss profile (5). (a) Spontaneous transformation of an unstable symmetric dipole into a fundamental soliton at p i =0.8 . (b) Stable propagation of the symmetric dipole at p i =1.8 . (c) The transformation of an unstable symmetric dipole into breather at p i =3.2 . (d,e) The stable propagation of the symmetric and asymmetric dipoles at p i =1.5 and p i =2.1 , respectively. (f) Spontaneous transformation of an unstable asymmetric dipole into a breather, with the dynamically restored symmetry, at p i =2.23 . All the cases are shown for σ i =3 , with small noise added to the input.

Equations (1)

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( b+i p i )w=(1/2) d 2 w/d η 2 +[ σ r iγ(η) ]w | w | 2 .

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