Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations

Details Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations

2006-10-04

arxiv.org/abs/math/0610133v1

Mathematics

Analysis of PDEs

to appear in Nonlinearity

Scientific paper

10.1088/0951-7715/19/12/002

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrodinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrodinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrodinger equations in two and three dimensional domains, we prove the existence of least energy solutions and study the location and configuration of symbiotic bright solitons. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.

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