We consider a two-component system of nonlinear Schrodinger equations with cubic nonlinearity and a trap potential, which is a model of the Bose-Einstein Condensation, in two space dimensions.
When the Planck constant is sufficiently small, we prove that the single-peak standing wave is orbitally stable for the case of attractive interaction between two components, while it is orbitally unstable for the case of repulsive interaction.
