Science and Mathematics Faculty Publications

Title

On Elliptic Solutions of a Coupled Nonlinear Schrödinger System

Document Type

Article

Publication Date

12-2013

Journal Title

Physica D: Nonlinear Phenomena

Volume

264

First Page

1

Last Page

16

Abstract

An explicit formula is obtained for single-phase bounded elliptic solutions of the Manakov system of integrable coupled nonlinear Schrödinger equations in terms of the Weierstrass sigma function with a real quasiperiod. The parametrization is effective in the sense that the reality conditions are completely characterized for each of the three possible couplings: focusing–focusing, defocusing–defocusing and focusing–defocusing. The Manakov soliton is recovered in the soliton limit and the small-wave-modulation limit is shown to satisfy the linearized dispersion relation of planewave solutions.

Keywords

Coupled nonlinear Schrödinger equation, Elliptic solutions, Integrable equation

Share

COinS