Coupled mode equations and gap solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential

PHYSICA D-NONLINEAR PHENOMENA

卷:238

Article

Dohnal, Tomas¹  Uecker, Hannes² 

[1] Univ Karlsruhe, Inst Angew & Numer Math 2, Karlsruhe, Germany

[2] Carl von Ossietzky Univ Oldenburg, Inst Math, Oldenburg, Germany

关键词: Gap solitons;    Coupled Mode Equations;    Periodic Nonlinear Schrodinger equation;    Gross-Pitaevskii equation;    Bloch wave analysis;    Lyapunov-Schmidt reduction;   

DOI  :  10.1016/j.physd.2009.02.013

来源: Elsevier

【 摘 要 】

Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schrodinger/Gross-Pitaevskii Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, G. Schneider, Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential, J. Nonlinear Sci. 19 (2009) 95-131] the CME derivation has to be carried out in Bloch rather than physical coordinates. Using the Lyapunov-Schmidt reduction we then give a rigorous justification of the CMEs as an asymptotic model for reversible non-degenerate gap solitons and provide HI estimates for this approximation. The results are confirmed by numerical examples, including some new families of CMEs and gap solitons absent for separable potentials. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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