Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential
نویسندگان
چکیده
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 Schrödinger / 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, and G. Schneider, J. Nonlin. Sci. (2008), online] 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 H estimates for this approximation. The results are confirmed by numerical examples including some new families of CMEs and gap solitons absent for separable potentials.
منابع مشابه
Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevsky equation with a non-separable periodic potential
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 Schrödinger / Gross-Pitaevsky Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, and G...
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