Remarks on the interface layer of a two-component Bose-Einstein condensate

TL;DR

This paper extends previous work on the interface behavior of two-component Bose-Einstein condensates to nonsymmetric cases, establishing existence and uniqueness of solutions in a Hamiltonian system framework.

Contribution

It generalizes prior symmetric case results to nonsymmetric scenarios and proves the uniqueness of the heteroclinic connection solutions.

Findings

Established existence of heteroclinic solutions in nonsymmetric cases

Proved uniqueness of these solutions

Extended the analytical approach to more general conditions

Abstract

We consider the heteroclinic connection problem for a class of Hamiltonian systems, containing a large competition parameter, which arise in the study of the behaviour of the wave functions of a two-component Bose-Einstein condensate near the interface, in the case of segregation. This problem was studied in detail recently in arXiv:1509.08328 under a symmetry assumption. Here, we extend the approach of the latter paper to the nonsymmetric case, to recover essentially the same result. Moreover, we establish a uniqueness result for such solutions.