Science and Mathematics Faculty Publications
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
Recommended Citation
Wright, Otis C. III, "On Elliptic Solutions of a Coupled Nonlinear Schrödinger System" (2013). Science and Mathematics Faculty Publications. 276.
https://digitalcommons.cedarville.edu/science_and_mathematics_publications/276