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Coupled Mode Equations and Gap Solitons in Higher Dimensions by Dohnal, Tomas; Wahlers, Lisa is a scholarly article available to read on EtoBox.

What is Coupled Mode Equations and Gap Solitons in Higher Dimensions about?

We study waves-packets in nonlinear periodic media in arbitrary ($d$) spatial dimension, modeled by the cubic Gross-Pitaevskii equation. In the asymptotic setting of small and broad waves-packets with $N\in \mathbb{N}$ carrier Bloch waves the effective equations for the envelopes are first order coupled mode equations (CMEs). We provide a rigorous justification of the effective equations. The estimate of the asymptotic error is carried out in an $L^1$-norm in the Bloch variables. This translates to a supremum norm estimate in the physical variables. In order to investigate the existence of gap solitons of the $d$-dimensional CMEs, we discuss spectral gaps of the CMEs. For $N=4$ and $d=2$ a family of time harmonic gap solitons is constructed formally asymptotically and numerically. Moving gap solitons have not been found for $d>1$ and for the considered values of $N$ due to the absence of a spectral gap in the standard moving frame variables.

Author

Dohnal, Tomas; Wahlers, Lisa

Published

2018

Language

EN