Quasi-periodic solutions of the coupled nonlinear Schrodinger equations

P L Christiansen, J C Eilbeck, V Z Enolskii, N A Kostov

Research output: Contribution to journalArticle

Abstract

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrodinger equations. In fibre optics these equations can be used to model single mode fibres under the action of cross-phase modulation, with weak birefringence. The problem is reduced to the '1:2:1' integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasi-periodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasi-periodic solutions to elliptic functions is discussed.

Original languageEnglish
Pages (from-to)685-700
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume451
Issue number1943
DOIs
Publication statusPublished - 8 Dec 1995

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