Date:	Mon, September 14, 2009
Time:	17:15
Place:	Research II Lecture Hall

Abstract: We start with a simple introduction to multi-scale analysis in nonlinear optics. Then we study gap solitons near a band edge of the 2D Periodic Nonlinear Schrödinger / Gross-Pitaevskii Equation with a non-separable potential of finite contrast, which can formally be approximated by solutions of Coupled Mode Equations (CMEs). Using Lyapunov-Schmidt reduction we give a rigorous justification of the CMEs as an asymptotic model for reversible non-degenerate gap solitons and provide H^s estimates for this approximation. The results are confirmed by numerical examples including some new families of CMEs and gap solitons absent for separable potentials.