Phase separating solutions for two component systems in general planar domains

TL;DR

This paper investigates the behavior of solutions to coupled nonlinear Schrödinger equations modeling phase separation in binary Bose-Einstein condensates, showing existence of solutions for large interspecies interaction parameters.

Contribution

It establishes the existence of solutions for large interspecies scattering length by reducing the problem to scalar equations on pure phase domains, under non-degeneracy conditions.

Findings

Existence of solutions for large scattering length parameter

Reduction to scalar problems on pure phase subdomains

Solutions parametrized by the interspecies interaction strength

Abstract

In this paper we consider a two component system of coupled non linear Schr\"odinger 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 $\beta$ the system reduces to a couple of scalar problems on subdomains of pure phases. 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 $\beta\gg 1$.