Location and phase segregation of ground and excited states for 2D Gross-Pitaevskii systems

We consider a system of Gross-Pitaevskii equations in R^2 modelling a mixture of two Bose-Einstein condensates with repulsive interaction. We aim to study the qualitative behaviour of ground and excited state solutions. We allow two different harmonic and off-centered trapping potentials and study the spatial patterns of the solutions within the Thomas-Fermi approximation as well as phase segregation phenomena within the large-interaction regime.