Abstract

We study both the stability and rotational dynamics of dissipative spatial solitons in optical media described by the cubic-quintic complex Ginzburg–Landau equation in the presence of periodic cylindrical lattices. We consider three kinds of cylindrical lattices, which are generated by (a) the refractive index modulation, (b) the linear-loss modulation, and (c) the combined modulation of both refractive index and linear-loss coefficient. The solitons can be trapped inside each concentric lattice ring (circular “trough”) and can be set into rotary motion by imposing onto the input field distribution a phase slope (or angle), which is proportional to the initial momentum imparted to the soliton in the tangential direction. The rotary motion can be effectively controlled by tuning the amplitude of the modulation profile. For either refractive index or linear-loss modulated cylindrical lattices, the spatial soliton can exhibit stably persistent rotation along the circular lattice orbit only if its initial momentum does not exceed a certain allowable maximum value. But for cylindrical lattices generated by combined refractive index modulation and linear-loss modulation, soliton rotary motion only appears in the initial propagation stage and then stops at certain spatial position. When the initial momentum imparted to the soliton is absent we find that for cylindrical lattices with only linear-loss modulation profile, by varying the modulation depth, the dissipative spatial soliton can display a transverse drift, can spread out into a stable multi-ring-shaped mode, or can decay.

© 2013 Optical Society of America

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  1. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary motion in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
    [CrossRef]
  2. Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
    [CrossRef]
  3. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef]
  4. Y. V. Kartashov, R. Carettero-Gonzaléz, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
    [CrossRef]
  5. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
    [CrossRef]
  6. X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
    [CrossRef]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. J. Phys. Special Topics 173, 87–105 (2009).
    [CrossRef]
  8. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
    [CrossRef]
  9. Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
    [CrossRef]
  10. 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. J. Phys. Special Topics 173, 233–243 (2009).
    [CrossRef]
  11. D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36, 1200–1202 (2011).
    [CrossRef]
  12. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).
    [CrossRef]
  13. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Symmetry breaking and multipeaked solitons in inhomogeneous gain landscapes,” Phys. Rev. A 83, 041806(R) (2011).
    [CrossRef]
  14. 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, 85–87 (2011).
    [CrossRef]
  15. O. V. Borovkova, Y. V. Kartashov, V. E. Lobanov, V. A. Vysloukh, and L. Torner, “Vortex twins and anti-twins supported by multi-ring gain landscapes,” Opt. Lett. 36, 3783–3785 (2011).
    [CrossRef]
  16. V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
    [CrossRef]
  17. Y. He and D. Mihalache, “Soliton drift or swing induced by spatially inhomogeneous losses in media described by the complex Ginzburg–Landau,” J. Opt. Soc. Am. B 29, 2554–2558 (2012).
    [CrossRef]
  18. H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
    [CrossRef]
  19. Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
    [CrossRef]
  20. Y. He and D. Mihalache, “Spatial solitons in parity-time-symmetric mixed linear-nonlinear optical lattices: recent theoretical results,” Rom. Rep. Phys. 64, 1243–1258 (2012).
  21. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).
  22. B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, 2005), pp. 157–160.
  23. B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
    [CrossRef]
  24. P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. B 6, R60–R75 (2004).
    [CrossRef]
  25. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
    [CrossRef]
  26. N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
    [CrossRef]
  27. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
    [CrossRef]
  28. H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
    [CrossRef]
  29. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
    [CrossRef]
  30. W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
    [CrossRef]
  31. W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26, 2204–2210 (2009).
    [CrossRef]
  32. I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
    [CrossRef]
  33. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
    [CrossRef]
  34. L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
    [CrossRef]
  35. Y. J. He, B. A. Malomed, F. W. Ye, and B. B. Hu, “Dynamics of dissipative spatial solitons over a sharp potential,” J. Opt. Soc. Am. B 27, 1139–1142 (2010).
    [CrossRef]
  36. D. Mihalache, “Topological dissipative nonlinear modes in two- and three-dimensional Ginzburg-Landau models with trapping potentials,” Rom. Rep. Phys. 63, 9–24 (2011).
  37. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
    [CrossRef]
  38. Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, “Stable surface solitons in truncated complex potentials,” Opt. Lett. 37, 2526–2528 (2012).
    [CrossRef]
  39. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
    [CrossRef]
  40. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
    [CrossRef]
  41. D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57, 352–371 (2012).
  42. Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
    [CrossRef]
  43. Y. V. Bludov and V. V. Konotop, “Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices,” Phys. Rev. A 81, 013625 (2010).
    [CrossRef]

2013 (2)

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

2012 (5)

Y. He and D. Mihalache, “Spatial solitons in parity-time-symmetric mixed linear-nonlinear optical lattices: recent theoretical results,” Rom. Rep. Phys. 64, 1243–1258 (2012).

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57, 352–371 (2012).

Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, “Stable surface solitons in truncated complex potentials,” Opt. Lett. 37, 2526–2528 (2012).
[CrossRef]

Y. He and D. Mihalache, “Soliton drift or swing induced by spatially inhomogeneous losses in media described by the complex Ginzburg–Landau,” J. Opt. Soc. Am. B 29, 2554–2558 (2012).
[CrossRef]

2011 (6)

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, 85–87 (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, 1200–1202 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, V. E. Lobanov, V. A. Vysloukh, and L. Torner, “Vortex twins and anti-twins supported by multi-ring gain landscapes,” Opt. Lett. 36, 3783–3785 (2011).
[CrossRef]

D. Mihalache, “Topological dissipative nonlinear modes in two- and three-dimensional Ginzburg-Landau models with trapping potentials,” Rom. Rep. Phys. 63, 9–24 (2011).

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

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

2010 (5)

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Y. J. He, B. A. Malomed, F. W. Ye, and B. B. Hu, “Dynamics of dissipative spatial solitons over a sharp potential,” J. Opt. Soc. Am. B 27, 1139–1142 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).
[CrossRef]

Y. V. Bludov and V. V. Konotop, “Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices,” Phys. Rev. A 81, 013625 (2010).
[CrossRef]

2009 (3)

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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. J. Phys. Special Topics 173, 87–105 (2009).
[CrossRef]

W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26, 2204–2210 (2009).
[CrossRef]

2008 (3)

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

2007 (3)

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
[CrossRef]

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

2006 (4)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef]

2005 (4)

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

Y. V. Kartashov, R. Carettero-Gonzaléz, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef]

2004 (2)

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. B 6, R60–R75 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary motion in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

2002 (1)

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

2001 (2)

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
[CrossRef]

1996 (1)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Afanasjev, V. V.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Akhmediev, N.

W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26, 2204–2210 (2009).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Aleksic, N. B.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Aranson, I. S.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
[CrossRef]

Bludov, Y. V.

Y. V. Bludov and V. V. Konotop, “Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices,” Phys. Rev. A 81, 013625 (2010).
[CrossRef]

Borovkova, O. V.

Carettero-Gonzaléz, R.

Chang, W.

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Chow, K. W.

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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
[CrossRef]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

Fedorov, S. V.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

Guo, L.

Haboucha, A.

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

He, Y.

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Y. He and D. Mihalache, “Soliton drift or swing induced by spatially inhomogeneous losses in media described by the complex Ginzburg–Landau,” J. Opt. Soc. Am. B 29, 2554–2558 (2012).
[CrossRef]

Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, “Stable surface solitons in truncated complex potentials,” Opt. Lett. 37, 2526–2528 (2012).
[CrossRef]

Y. He and D. Mihalache, “Spatial solitons in parity-time-symmetric mixed linear-nonlinear optical lattices: recent theoretical results,” Rom. Rep. Phys. 64, 1243–1258 (2012).

He, Y. J.

Y. J. He, B. A. Malomed, F. W. Ye, and B. B. Hu, “Dynamics of dissipative spatial solitons over a sharp potential,” J. Opt. Soc. Am. B 27, 1139–1142 (2010).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
[CrossRef]

Hu, B. B.

Kartashov, Y. V.

Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, “Stable surface solitons in truncated complex potentials,” Opt. Lett. 37, 2526–2528 (2012).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (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, 85–87 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, V. E. Lobanov, V. A. Vysloukh, and L. Torner, “Vortex twins and anti-twins supported by multi-ring gain landscapes,” Opt. Lett. 36, 3783–3785 (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, 041806(R) (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, 1200–1202 (2011).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. J. Phys. Special Topics 173, 87–105 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Y. V. Kartashov, R. Carettero-Gonzaléz, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary motion in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Komarov, A.

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

Konotop, V. V.

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett. 36, 1200–1202 (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, 041806(R) (2011).
[CrossRef]

Y. V. Bludov and V. V. Konotop, “Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices,” Phys. Rev. A 81, 013625 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).
[CrossRef]

Kramer, L.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Leblond, H.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

Ling, D.

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Liu, J.

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Lobanov, V. E.

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

Y. J. He, B. A. Malomed, F. W. Ye, and B. B. Hu, “Dynamics of dissipative spatial solitons over a sharp potential,” J. Opt. Soc. Am. B 27, 1139–1142 (2010).
[CrossRef]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
[CrossRef]

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Y. V. Kartashov, R. Carettero-Gonzaléz, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
[CrossRef]

B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, 2005), pp. 157–160.

Mandel, P.

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. B 6, R60–R75 (2004).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

Mihalache, D.

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57, 352–371 (2012).

Y. He and D. Mihalache, “Spatial solitons in parity-time-symmetric mixed linear-nonlinear optical lattices: recent theoretical results,” Rom. Rep. Phys. 64, 1243–1258 (2012).

Y. He and D. Mihalache, “Soliton drift or swing induced by spatially inhomogeneous losses in media described by the complex Ginzburg–Landau,” J. Opt. Soc. Am. B 29, 2554–2558 (2012).
[CrossRef]

Y. He, D. Mihalache, X. Zhu, L. Guo, and Y. V. Kartashov, “Stable surface solitons in truncated complex potentials,” Opt. Lett. 37, 2526–2528 (2012).
[CrossRef]

D. Mihalache, “Topological dissipative nonlinear modes in two- and three-dimensional Ginzburg-Landau models with trapping potentials,” Rom. Rep. Phys. 63, 9–24 (2011).

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Musslimani, Z. H.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Rosanov, N. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
[CrossRef]

Salhi, M.

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

Sanchez, F.

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Shatsev, A. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

Skarka, V.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Taki, M.

Tlidi, M.

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. B 6, R60–R75 (2004).
[CrossRef]

Torner, L.

O. V. Borovkova, Y. V. Kartashov, V. E. Lobanov, V. A. Vysloukh, and L. Torner, “Vortex twins and anti-twins supported by multi-ring gain landscapes,” Opt. Lett. 36, 3783–3785 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (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, 85–87 (2011).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. J. Phys. Special Topics 173, 87–105 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

Y. V. Kartashov, R. Carettero-Gonzaléz, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary motion in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Town, G.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

Vysloukh, V. A.

Wabnitz, S.

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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Wang, H.

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Wang, H. Z.

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
[CrossRef]

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Ye, F. W.

Zezyulin, D. A.

Zhu, W.

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Zhu, X.

Appl. Phys. B (1)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Universal properties of self-organized localized structures,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

Chaos (1)

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg–Landau equations,” Chaos 17, 037117 (2007).
[CrossRef]

Eur. J. Phys. Special Topics (2)

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. J. Phys. Special Topics 173, 233–243 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. J. Phys. Special Topics 173, 87–105 (2009).
[CrossRef]

J. Opt. A (1)

H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, “Cis bound states of three localized states of the cubic-quintic CGL equation,” J. Opt. A 8, 319–326 (2006).
[CrossRef]

J. Opt. B (2)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. B 6, R60–R75 (2004).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

Y. J. He, B. A. Malomed, D. Mihalache, and H. Z. Wang, “Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates,” J. Phys. B 41, 055301 (2008).
[CrossRef]

Nat. Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Opt. Commun. (1)

H. Wang, W. Zhu, J. Liu, D. Ling, and Y. He, “Manipulating solitons by antisymmetric inhomogeneous loss in the complex Ginzburg–Landau model,” Opt. Commun. 306, 160–164 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (6)

Y. V. Bludov and V. V. Konotop, “Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices,” Phys. Rev. A 81, 013625 (2010).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (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, 041806(R) (2011).
[CrossRef]

Y. He and D. Mihalache, “Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials,” Phys. Rev. A 87, 013812 (2013).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Steering the motion of rotary solitons in radial lattices,” Phys. Rev. A 76, 053601 (2007).
[CrossRef]

Phys. Rev. E (4)

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E 74, 066615 (2006).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses,” Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal optical solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary motion in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Rev. Mod. Phys. (2)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Rom. J. Phys. (1)

D. Mihalache, “Linear and nonlinear light bullets: recent theoretical and experimental studies,” Rom. J. Phys. 57, 352–371 (2012).

Rom. Rep. Phys. (2)

D. Mihalache, “Topological dissipative nonlinear modes in two- and three-dimensional Ginzburg-Landau models with trapping potentials,” Rom. Rep. Phys. 63, 9–24 (2011).

Y. He and D. Mihalache, “Spatial solitons in parity-time-symmetric mixed linear-nonlinear optical lattices: recent theoretical results,” Rom. Rep. Phys. 64, 1243–1258 (2012).

Other (2)

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).

B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, 2005), pp. 157–160.

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Figures (4)

Fig. 1.
Fig. 1.

Soliton stability and its rotary motion within the first annular trough of the cylindrical lattice with only refractive index modulation and for R(r)=3cos2(r) and L(r)=0. (a) The input soliton located at the first annular trough of the cylindrical lattice. (b) Soliton power P versus refractive index modulation depth R0. (c) Allowable maximum value Mmax of the initial linear momentum imparted to the soliton in the tangential direction versus refractive index modulation depth R0. Region above the solid curve: unstable soliton rotary motion; region below the solid curve: stable soliton rotary motion. (d) Stationary soliton trapped at the first annular trough of the cylindrical lattice for zero input linear momentum (M=0) corresponding to point A in (b). (e) and (f) Stable soliton rotary motion for M=2 and unstable soliton rotary motion for M=4, respectively, corresponding to points B and C in (c). The input soliton position is at xin=π.

Fig. 2.
Fig. 2.

Soliton rotary motion within the first annular trough of the lattice with only linear-loss modulation for L(r)=L0sin(2r) and R(r)=0. (a) Allowable maximum value Mmax of the initial momentum imparted to the soliton in the tangential direction versus linear-loss modulation depth L0. Region above the solid curve: unstable soliton rotary motion; region below the solid curve: stable soliton rotary motion. (b) Input soliton, which is located at the first annular trough of the lattice. (c) Stable soliton rotary motion for M=0.3 and L0=0.5 and (d) unstable soliton rotary motion for M=0.4 and L0=0.5, respectively, corresponding to points A and B in (a). The input soliton position is at xin=3π/4.

Fig. 3.
Fig. 3.

Evolution scenarios of a soliton located at first annular trough of the lattice with only loss modulation profile [L(r)=L0sin(2r) and R(r)=0], for the case of zero input momentum imparted on the soliton (M=0). (a) Soliton crossing the lattice for L0=0.1. (b) Soliton decay for L0=0.3. (c) The stationary soliton evolution for L0=0.4. (d) Evolution of unstable soliton for L0=1. (e) Soliton evolving into a ring-shaped beam for L0=10.

Fig. 4.
Fig. 4.

Soliton rotary motion within the first annular trough of the cylindrical lattices with combined refractive index modulation profile R(r)=R0cos2(r) and loss modulation profile L(r)=L0sin(2r). (a) Maximum allowable momentum Mmax versus loss modulation depth L0. (b) Maximum allowable momentum Mmax versus refractive index modulation depth R0. In (a) and (b), above the solid curves: unstable soliton rotary motion; below the solid curves: stable soliton rotary motion. (c) Stable soliton evolution for M=1, R0=6, L0=0.5 and (d) unstable soliton evolution for M=2, R0=6, L0=0.5, respectively, corresponding to points A and B in (a) and (b). The input position of the soliton is at xin=π.

Equations (1)

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iuz+(1/2)(uxx+uyy)+|u|2u+ν|u|4u=iN[u][R(r)+iL(r)]u,

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