Abstract
Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solutions. Here we show that there exist symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrödinger 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 behaviour by some techniques of singular perturbation problems.
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