Standing waves for coupled nonlinear Schrodinger equations with decaying potentials

We study the following singularly perturbed problem for a coupled nonlinear Schrodinger system which arises in Bose-Einstein condensate: -epsilon(2)Delta u + a(x) u = mu(1)mu(3) + beta uv(2) and -epsilon(2)Delta v + b(x) v = mu(2)v(3) + beta u(2)v in R-3 with u, v > 0 and u(x), v(x) -> 0 as vertical bar x vertical bar -> infinity. Here, a, b are non-negative continuous potentials, and mu(1), mu(2) > 0. We consider the case where the coupling constant beta > 0 is relatively large. Then for sufficiently small epsilon > 0, we obtain positive solutions of this system which concentrate around local minima of the potentials as epsilon -> 0. The novelty is that the potentials a and b may vanish at someplace and decay to 0 at infinity. (C) 2013 AIP Publishing LLC.