Abstract

We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schrödinger equations, coupled by repulsive XPM (cross-phase-modulation) terms, in the absence of the SPM (self-phase-modulation) nonlinearity. The equations include a periodic potential acting on both components, thus giving rise to GSs of the “symbiotic” type, which exist solely due to the repulsive interaction between the two components. The model may be implemented for “holographic solitons” in optics, and in binary bosonic or fermionic gases trapped in the optical lattice. Fundamental symbiotic GSs are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. Symmetric solitons are destabilized, including their entire family in the second bandgap, by symmetry-breaking perturbations above a critical value of the total power. Asymmetric solitons of intra-gap and inter-gap types are studied too, with the propagation constants of the two components falling into the same or different bandgaps, respectively. The increase of the asymmetry between the components leads to shrinkage of the stability areas of the GSs. Inter-gap GSs are stable only in a strongly asymmetric form, in which the first-bandgap component is a dominating one. Intra-gap solitons are unstable in the second bandgap. Unstable two-component GSs are transformed into persistent breathers. In addition to systematic numerical considerations, analytical results are obtained by means of an extended (“tailed”) Thomas-Fermi approximation (TFA).

© 2012 OSA

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    [CrossRef]
  3. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
    [CrossRef]
  4. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattice,” Rev. Mod. Phys.83, 247–306 (2011).
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    [CrossRef] [PubMed]
  10. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
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    [CrossRef]
  14. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
    [CrossRef]
  15. H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B37, 1443–1459 (2004).
    [CrossRef]
  16. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
    [CrossRef]
  17. V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B18, 627–651 (2004).
    [CrossRef]
  18. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett.63, 642–648 (2003).
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  19. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett.28, 2094–2096 (2003).
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  21. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
    [CrossRef]
  22. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
    [CrossRef]
  23. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
    [CrossRef]
  24. B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
    [CrossRef]
  25. T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
    [CrossRef]
  26. K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
    [CrossRef]
  27. D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
    [CrossRef]
  28. G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
    [CrossRef]
  29. J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
    [CrossRef]
  30. Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
    [CrossRef]
  31. A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
    [CrossRef]
  32. S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A77, 023607 (2008).
    [CrossRef]
  33. V. M. Pérez-García and J. B. Beitia, “Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A72, 033620 (2005).
    [CrossRef]
  34. S. K. Adhikari, “Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation,” Phys. Lett. A346, 179–185 (2005).
    [CrossRef]
  35. S. K. Adhikari, “Fermionic bright soliton in a boson-fermion mixture,” Phys. Rev. A72, 053608 (2005).
    [CrossRef]
  36. S. K. Adhikari and B. A. Malomed, “Two-component gap solitons with linear interconversion,” Phys. Rev. A79, 015602 (2009).
    [CrossRef]
  37. O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
    [CrossRef]
  38. M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
    [CrossRef]
  39. O. Cohen, T. Carmon, M. Segev, and S. Odoulov, “Holographic solitons,” Opt. Lett.27, 2031–2033 (2002).
    [CrossRef]
  40. O. Cohen, M. M. Murnane, H. C. Kapteyn, and M. Segev, “Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefractives,” Opt. Lett.31, 954–956 (2006).
    [CrossRef] [PubMed]
  41. J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, “Spatial optical solitons supported by mutual focusing,” Opt. Lett.28, 1457–1459 (2003).
  42. J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
    [CrossRef]
  43. S. Adhikari and B. A. Malomed, “Gap solitons in a model of a superfluid fermion gas in optical lattices,” Physica D238, 1402–1412 (2009).
    [CrossRef]
  44. N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67, 063608 (2003).
    [CrossRef]
  45. T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A74, 033616 (2006).
    [CrossRef]
  46. J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
    [CrossRef]

2011 (2)

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

G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
[CrossRef]

2010 (1)

O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
[CrossRef]

2009 (6)

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Two-component gap solitons with linear interconversion,” Phys. Rev. A79, 015602 (2009).
[CrossRef]

S. Adhikari and B. A. Malomed, “Gap solitons in a model of a superfluid fermion gas in optical lattices,” Physica D238, 1402–1412 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

2008 (3)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A77, 023607 (2008).
[CrossRef]

2007 (2)

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
[CrossRef]

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

2006 (7)

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A74, 033616 (2006).
[CrossRef]

O. Cohen, M. M. Murnane, H. C. Kapteyn, and M. Segev, “Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefractives,” Opt. Lett.31, 954–956 (2006).
[CrossRef] [PubMed]

A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
[CrossRef]

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

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

2005 (5)

A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, and A. Tünnermann, 2005, “Discrete nonlinear localization in femtosecond laser written waveguides in fused silica,” Opt. Express13, 10552–10557 (2005).
[CrossRef] [PubMed]

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

V. M. Pérez-García and J. B. Beitia, “Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A72, 033620 (2005).
[CrossRef]

S. K. Adhikari, “Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation,” Phys. Lett. A346, 179–185 (2005).
[CrossRef]

S. K. Adhikari, “Fermionic bright soliton in a boson-fermion mixture,” Phys. Rev. A72, 053608 (2005).
[CrossRef]

2004 (6)

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B37, 1443–1459 (2004).
[CrossRef]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
[CrossRef]

Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B21, 973–981 (2004).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B18, 627–651 (2004).
[CrossRef]

2003 (5)

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

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

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, “Spatial optical solitons supported by mutual focusing,” Opt. Lett.28, 1457–1459 (2003).

N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67, 063608 (2003).
[CrossRef]

2002 (4)

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, “Holographic solitons,” Opt. Lett.27, 2031–2033 (2002).
[CrossRef]

K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose–Einstein condensates induced by modulational instability,” J. Phys. B: At. Mol. Opt. Phys.35, 5105–5119 (2002).
[CrossRef]

Adhikari, S.

S. Adhikari and B. A. Malomed, “Gap solitons in a model of a superfluid fermion gas in optical lattices,” Physica D238, 1402–1412 (2009).
[CrossRef]

Adhikari, S. K.

S. K. Adhikari and B. A. Malomed, “Two-component gap solitons with linear interconversion,” Phys. Rev. A79, 015602 (2009).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A77, 023607 (2008).
[CrossRef]

S. K. Adhikari, “Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation,” Phys. Lett. A346, 179–185 (2005).
[CrossRef]

S. K. Adhikari, “Fermionic bright soliton in a boson-fermion mixture,” Phys. Rev. A72, 053608 (2005).
[CrossRef]

Akylas, T. R.

G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
[CrossRef]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

Baizakov, B.

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

Baizakov, B. B.

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
[CrossRef]

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

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose–Einstein condensates induced by modulational instability,” J. Phys. B: At. Mol. Opt. Phys.35, 5105–5119 (2002).
[CrossRef]

Beitia, J. B.

V. M. Pérez-García and J. B. Beitia, “Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A72, 033620 (2005).
[CrossRef]

Blömer, D.

Borovkova, O. V.

O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B18, 627–651 (2004).
[CrossRef]

Burghoff, J.

Carmon, T.

Chen, Z.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67, 063608 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Cohen, O.

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Cuevas, J.

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

Dickerscheid, D. B. M.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer: Dordrecht, 2009).

Efremidis, N. K.

N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67, 063608 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Fleischer, J. W.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Frantzeskakis, D. J.

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

Gubbels, K. B.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer: Dordrecht, 2009).

Gubeskys, A.

A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
[CrossRef]

Hilligsoe, K. M.

K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
[CrossRef]

Hwanga, G.

G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press: Princeton, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press: Princeton, 2008).

Kapteyn, H. C.

Kartashov, Y. V.

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

O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Kevrekidis, P. G.

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

Kivshar, Y. S.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
[CrossRef]

J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, “Spatial optical solitons supported by mutual focusing,” Opt. Lett.28, 1457–1459 (2003).

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

Konotop, V. V.

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B18, 627–651 (2004).
[CrossRef]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose–Einstein condensates induced by modulational instability,” J. Phys. B: At. Mol. Opt. Phys.35, 5105–5119 (2002).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Liu, J.

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

Liu, S.

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

Malomed, B. A.

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

O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Two-component gap solitons with linear interconversion,” Phys. Rev. A79, 015602 (2009).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

S. Adhikari and B. A. Malomed, “Gap solitons in a model of a superfluid fermion gas in optical lattices,” Physica D238, 1402–1412 (2009).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A77, 023607 (2008).
[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
[CrossRef]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A74, 033616 (2006).
[CrossRef]

A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

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

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B37, 1443–1459 (2004).
[CrossRef]

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

Marzlin, K. P.

K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
[CrossRef]

Matuszewski, M.

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
[CrossRef]

Mayteevarunyoo, T.

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A74, 033616 (2006).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press: Princeton, 2008).

Merhasin, I. M.

A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
[CrossRef]

Mihalache, D.

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

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Morsch, O.

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

Murnane, M. M.

Musslimani, Z. H.

Nolte, S.

Oberthaler, M.

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

Oberthaler, M. K.

K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
[CrossRef]

Odoulov, S.

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
[CrossRef]

D. E. Pelinovsky, Localization in Periodic Potentials (Cambridge University Press: Cambridge, UK, 2011).
[CrossRef]

Pérez-García, V. M.

V. M. Pérez-García and J. B. Beitia, “Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A72, 033620 (2005).
[CrossRef]

Pertsch, T.

Pitaevskii, L.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensate (Clarendon Press: Oxford, 2003).

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B37, 1443–1459 (2004).
[CrossRef]

Salerno, M.

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
[CrossRef]

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

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose–Einstein condensates induced by modulational instability,” J. Phys. B: At. Mol. Opt. Phys.35, 5105–5119 (2002).
[CrossRef]

Salgueiro, J. R.

Savage, C. M.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

Schreiber, T.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

O. Cohen, M. M. Murnane, H. C. Kapteyn, and M. Segev, “Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefractives,” Opt. Lett.31, 954–956 (2006).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, “Holographic solitons,” Opt. Lett.27, 2031–2033 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Shi, Z.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

Stoof, H. T. C.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer: Dordrecht, 2009).

Stringari, S.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensate (Clarendon Press: Oxford, 2003).

Sukhorukov, A. A.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
[CrossRef]

J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, “Spatial optical solitons supported by mutual focusing,” Opt. Lett.28, 1457–1459 (2003).

Szameit, A.

Torner, L.

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
[CrossRef]

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

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

Trippenbach, M.

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
[CrossRef]

Tünnermann, A.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
[CrossRef]

Wang, C.

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

Wang, J.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press: Princeton, 2008).

Wise, F.

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

Yang, J.

G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B21, 973–981 (2004).
[CrossRef]

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

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM: Philadelphia, 2010).
[CrossRef]

Zhang, G.

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

J. Liu, S. Liu, G. Zhang, and C. Wang, “Observation of two-dimensional holographic photovoltaic bright solitons in a photorefractive-photovoltaic crystal,” Appl. Phys. Lett.91, 111113 (2007).
[CrossRef]

EPL (1)

O. V. Borovkova, B. A. Malomed, and Y. V. Kartashov, “Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component,” EPL92, 64001 (2010).
[CrossRef]

Eur. Phys. J. (1)

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional semi-gap solitons in a periodic potential,” Eur. Phys. J.38, 367–374 (2006).
[CrossRef]

Europhys. Lett. (1)

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

J. Opt. B: Quant. Semicl. Opt. (1)

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

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B37, 1443–1459 (2004).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose–Einstein condensates induced by modulational instability,” J. Phys. B: At. Mol. Opt. Phys.35, 5105–5119 (2002).
[CrossRef]

Mod. Phys. Lett. B (1)

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B18, 627–651 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Lett. A (1)

S. K. Adhikari, “Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation,” Phys. Lett. A346, 179–185 (2005).
[CrossRef]

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete Solitons in Optics,” Phys. Rep.463, 1 (2008).
[CrossRef]

Phys. Rev. A (14)

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, “Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,” Phys. Rev. A67, 013602 (2003).
[CrossRef]

S. K. Adhikari, “Fermionic bright soliton in a boson-fermion mixture,” Phys. Rev. A72, 053608 (2005).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Two-component gap solitons with linear interconversion,” Phys. Rev. A79, 015602 (2009).
[CrossRef]

K. M. Hilligsoe, M. K. Oberthaler, and K. P. Marzlin, “Stability of gap solitons in a Bose-Einstein condensate,” Phys. Rev. A66, 063605 (2002).
[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A76, 043826 (2007).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A70, 053613 (2004).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A78, 063812 (2008).
[CrossRef]

A. Gubeskys, B. A. Malomed, and I. M. Merhasin, “Two-component gap solitons in two- and one-dimensional Bose-Einstein condensate,” Phys. Rev. A73, 023607 (2006).
[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A77, 023607 (2008).
[CrossRef]

V. M. Pérez-García and J. B. Beitia, “Symbiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A72, 033620 (2005).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67, 063608 (2003).
[CrossRef]

T. Mayteevarunyoo and B. A. Malomed, “Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice,” Phys. Rev. A74, 033616 (2006).
[CrossRef]

J. Cuevas, B. A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis, “Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions,” Phys. Rev. A79, 053608 (2009).
[CrossRef]

Phys. Rev. E (5)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E70, 055603(R) (2004).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, “Bifurcations and stability of gap solitons in periodic potentials,” Phys. Rev. E70, 036618 (2004).
[CrossRef]

B. Baizakov, B. A. Malomed, and M. Salerno, “Matter-wave solitons in radially periodic potentials,” Phys. Rev. E74, 066615 (2006).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E66, 046602 (2002).
[CrossRef]

Physica D (3)

G. Hwanga, T. R. Akylas, and J. Yang, “Gap solitons and their linear stability in one-dimensional periodic media,” Physica D240, 1055–1068 (2011).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009).
[CrossRef]

S. Adhikari and B. A. Malomed, “Gap solitons in a model of a superfluid fermion gas in optical lattices,” Physica D238, 1402–1412 (2009).
[CrossRef]

Progr. Opt. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progr. Opt.52, 63–148 (2009).
[CrossRef]

Rev. Mod. Phys. (2)

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

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

Other (5)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press: Princeton, 2008).

L. Pitaevskii and S. Stringari, Bose-Einstein Condensate (Clarendon Press: Oxford, 2003).

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer: Dordrecht, 2009).

J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM: Philadelphia, 2010).
[CrossRef]

D. E. Pelinovsky, Localization in Periodic Potentials (Cambridge University Press: Cambridge, UK, 2011).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

The identical bandgap structures produced by the linearization of Eqs. (4) and (5) for ε = 6. Shaded areas are occupied by the Bloch bands, where gap solitons do not exist.

Fig. 2
Fig. 2

(a) The continuous (blue) curves show the numerically found amplitude of the fundamental symmetric gap solitons (with equal components), versus propagation constant k = q, in the first and second bandgaps at ε = 6.0. The chain of symbols is the analytical approximation for the same dependence, as produced by the improved TFA in the form of Eq. (16). The dashed curve is the result of the usual TFA, which corresponds to Eq. (16) without the correction (second) terms. (b) Total power P for the same soliton families, whose stable and unstable portions are designated by the bold dotted and dashed lines, respectively. The latter one is destabilized by symmetry-breaking perturbations, while the entire family is stable in the framework of the single-component model. Coordinates of the stability/instability border are given by Eq. (21). The chain of squares shows the analytical dependence produced by the TFA, see Eq. (20).

Fig. 3
Fig. 3

The evolution of a weakly unstable single-component fundamental soliton at k = −3.7.

Fig. 4
Fig. 4

Examples of fundamental symmetric gap solitons found in the first and second bandgaps, for k = q = 2.0 and k = q = −2.0 (left and right panels, respectively). Here and in similar figures below, the background pattern (green sinusoid) represents the underlying periodic potential. Both solitons are stable as solutions of the single-component model, but only the one corresponding to k = q = 2.0 remains stable in the two-component system, while its counterpart pertaining to k = q = −2 is destabilized by symmetry-breaking perturbations.

Fig. 5
Fig. 5

(a) and (b) The spontaneous transformation of an unstable symmetric fundamental soliton for u- and v-component, in the first bandgap, with k = q = 0, into a stable asymmetric breather. (c) The top and bottom plots display, respectively, the evolution of the peak-power difference, max(|u(x,z)|2) − max(|u(x,z)|2), and the separation between centers of the two components, Xu and Xv, which as per Eq. (22).

Fig. 6
Fig. 6

(a,b) The same as in Fig. 5(a,b), but for an unstable soliton in the second bandgap, with k = q = −3.5.

Fig. 7
Fig. 7

Examples of stable solitons of the intra-gap type found in the first finite bandgap, with fixed asymmetry R = −0.5: (a) k = 3 and q = 3.4601; (b) k = 1 and q = 2.843; (c) k = −0.5 and q = 2.5116. Fields U(x) and V(x), which pertain to propagation constants k and q, are shown, respectively, by the magenta (lower) and blue (higher) profiles.

Fig. 8
Fig. 8

The asymmetry ratio, R [defined as per Eq. (7)], versus propagation constant q, at fixed values of k = 3.0, 1.0, and k = −0.5 (the top, middle, and bottom curves, respectively), for asymmetric fundamental solitons of the intra-gap type. Stable and unstable branches are shown by solid and dashed lines, respectively.

Fig. 9
Fig. 9

An example of a stable strongly asymmetric soliton with k = −0.5 and q = 3.65. Fields U(x) and V(x), which pertain to propagation constants k and q, are shown, respectively, by the magenta (lower) and blue (taller) profiles.

Fig. 10
Fig. 10

A typical example of the transformation of the unstable asymmetric gap solitons into a breather, for k = −0.5 and q = 2.0.

Fig. 11
Fig. 11

(a) The stability border in the plane of the propagation constants, (k,q), for asymmetric solitons of the intra-gap type. Only half of the plane is shown, delineated by the dotted triangle, within which wavenumbers k and q belong to the first finite bandgap, as the other half is a mirror image of the displayed one. (b) The same in the plane of the total power and asymmetry ratio, (P,R), defined as per Eqs. (6) and (7). Localized modes do not exist above the right boundary of the stability regions in panel (b). The diagram at R < 0 is a mirror image of the one displayed here for R > 0.

Fig. 12
Fig. 12

An example of a stable inter-gap soliton, for k = 3 and q = −1.65. The single-peak and split-peak profiles, U(x) and V(x), represent, respectively, the components in the first and second finite bandgaps.

Fig. 13
Fig. 13

A typical example of the transformation of an unstable intergap soliton into a stable breather, at k = 0 and q = −2. (a,b) The evolution of |u|2 and |v|2. (c) The initial profiles of U(x) and V(x) (single-peak and split-peak shapes, respectively).

Fig. 14
Fig. 14

Asymmetry ratio R for the inter-gap solitons versus propagation constant q in the second finite bandgap, at fixed values k = 3.0, 2.5, 1.0, and −0.5 (from the top to the bottom) of wavenumber k in the first bandgap. Solid and dashed lines designate stable stationary solitons and breathers, respectively.

Fig. 15
Fig. 15

The same as in Fig. 11, but for inter-gap solitons. In (a), the dotted rectangle delineates the region occupied by wavenumbers k and q belonging to the first and second finite bandgaps, respectively.

Equations (22)

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i u z + 1 2 2 u x 2 | v | 2 u + ε cos ( 2 x ) u = 0 ,
i v z + 1 2 2 v x 2 | u | 2 v + ε cos ( 2 x ) v = 0 .
u ( x , z ) = e i k z U ( x ) , v ( x , z ) = e i q z V ( x ) ,
k U + 1 2 U V 2 U + ε cos ( 2 x ) U = 0 ,
q V + 1 2 V U 2 V + ε cos ( 2 x ) V = 0 ,
P = + ( | U | 2 + | V | 2 ) d x P u + P v ,
R = ( P u P v ) / ( P u + P v ) .
k max ( ε = 6 ) 3.75 .
u ( x , z ) = e i k z [ U ( x ) + u 1 ( x ) e i λ z + u 2 * ( x ) e i λ * z ] , v ( x , z ) = e i q z [ V ( x ) + v 1 ( x ) e i λ z + v 2 * ( x ) e i λ * z ] ,
q v 1 1 2 v 1 + U 2 ( x ) v 1 + U ( x ) V ( x ) ( u 1 + u 2 ) ε cos ( 2 x ) v 1 = λ v 1 ,
q v 2 + 1 2 v 2 U 2 ( x ) v 2 U ( x ) V ( x ) ( u 1 + u 2 ) + ε cos ( 2 x ) v 2 = λ v 2 ,
k u 1 1 2 u 1 + V 2 ( x ) u 1 + U ( x ) V ( x ) ( v 1 + v 2 ) ε cos ( 2 x ) u 1 = λ u 1 ,
k u 2 + 1 2 u 2 V 2 ( x ) u 2 U ( x ) V ( x ) ( v 1 + v 2 ) + ε cos ( 2 x ) u 2 = λ u 2 .
{ U 2 ( x ) V 2 ( x ) } inner = { ε cos ( 2 x ) q ε cos ( 2 x ) k } , at | x | < x 0 1 2 cos 1 ( k ε ) .
{ U ( x ) V ( x ) } { ε q ( ε / ε q ) x 2 , ε k ( ε / ε k ) x 2 . }
{ U ( x = 0 ) V ( x = 0 ) } { ε q ε [ 2 ( ε k ) ε q ] 1 , ε k ε [ 2 ( ε q ) ε k ] 1 , }
ε ( ε k ) ( ε q ) .
{ U 2 ( x ) } outer = { [ k q ( ε 2 k 2 ) / ( k q ) ( | x | x 0 ) ] 2 , at 0 < | x | x 0 < ( k q ) / ε 2 k 2 ; 0 , at | x | x 0 > ( k q ) / ε 2 k 2 . }
{ P u P v } TFA = { ε 2 k 2 q cos 1 ( k / ε ) + ( 2 / 3 ) ( k q ) 2 / ε 2 k 2 ; ε 2 k 2 k cos 1 ( k / ε ) . }
P ( k = q ) = 2 [ ε 2 k 2 k cos 1 ( k / ε ) ] ,
P cr 7.19 , k cr 1.05 ,
X u X v 1 P u + | u ( x , z ) | 2 x d x 1 P v + | v ( x , z ) | 2 x d x .

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