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We investigate the modulational instability of a two-dimensional Bose-Einstein condensate in a two-dimensional optical lattice using a time-dependent variational approach. Within this framework, we derive the ordinary differential equations for time evolution of the amplitude and phase of modulational perturbations. Analyzing these equations and the Hamiltonian of the system, we obtain the modulational instability criterion.
[1] Sulem C, Sulem P L 1999 The Nonlinear Schrödinger Equation (Spinger-Verlag,New York)
[2] Gross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3] Yang X X, Wu Y 2002 Chin. Phys. Lett. 19 1413
[4] Wu L, Zhang J F 2007 Chin. Phys. Lett. 24 1471
[5] Li S C, Duan W S 2009 Chin. Phys. B 18 4177
[6] Baizakov B B, Bouketir A, Messikh A 2009 Phys. Rev. E 79 046605
[7] Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[8] Zhao X D, Xie Z W, Zhang W P 2007 Phys. Rev. B 76 214408
[9] 2012 Phys Rev. E 86 017601
[10] Yu D S, Chen J B 2008 Chin. Phys. Lett. 25 1792
[11] 2014 Phys Rev. E 89 052917
[12] Rapti Z, Kevrekidis P G, Smerzi A, Bishop A R 2004 Phys. Rev. E 69 017601
[13] 2008 77 046216 (in Chinese) [Wamba E, Mohamadou A, Kofané T C, 2008 Phys Rev. E 77 046216]
[14] Jia L L, Sun S L, Li J H 2012 Acta Sinica Quantum Optica 18 65 (in Chinese) [贾磊磊, 孙山林, 李精华 2012 量子光学学报 18 65]
[15] Zhang H, Duan W S 2013 Acta Phys. Sin. 62 044703 (in Chinese) [张恒, 段文山 2013 62 044703]
[16] Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 57 3435]
[17] Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
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[1] Sulem C, Sulem P L 1999 The Nonlinear Schrödinger Equation (Spinger-Verlag,New York)
[2] Gross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3] Yang X X, Wu Y 2002 Chin. Phys. Lett. 19 1413
[4] Wu L, Zhang J F 2007 Chin. Phys. Lett. 24 1471
[5] Li S C, Duan W S 2009 Chin. Phys. B 18 4177
[6] Baizakov B B, Bouketir A, Messikh A 2009 Phys. Rev. E 79 046605
[7] Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[8] Zhao X D, Xie Z W, Zhang W P 2007 Phys. Rev. B 76 214408
[9] 2012 Phys Rev. E 86 017601
[10] Yu D S, Chen J B 2008 Chin. Phys. Lett. 25 1792
[11] 2014 Phys Rev. E 89 052917
[12] Rapti Z, Kevrekidis P G, Smerzi A, Bishop A R 2004 Phys. Rev. E 69 017601
[13] 2008 77 046216 (in Chinese) [Wamba E, Mohamadou A, Kofané T C, 2008 Phys Rev. E 77 046216]
[14] Jia L L, Sun S L, Li J H 2012 Acta Sinica Quantum Optica 18 65 (in Chinese) [贾磊磊, 孙山林, 李精华 2012 量子光学学报 18 65]
[15] Zhang H, Duan W S 2013 Acta Phys. Sin. 62 044703 (in Chinese) [张恒, 段文山 2013 62 044703]
[16] Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 57 3435]
[17] Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
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