  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.
