Phase separating solutions for two component systems in general planar domains

Abstract

In this paper we consider a two component system of coupled non linear Schrödinger equations modeling the phase separation in the binary mixture of Bose-Einstein condensates and other related problems. Assuming the existence of solutions in the limit of large interspecies scattering length β the system reduces to a couple of scalar problems on subdomains of pure phases [13]. Here we show that given a solution to the limiting problem under some additional non degeneracy assumptions there exists a family of solutions parametrized by the parameter β ≫ 1.