Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials

Recently, two-component systems of nonlinear Schrödinger equations with trap potentials have been well-known to describe a binary mixture of Bose-Einstein condensates called a double condensate. In a double condensate, the locations of spikes can be influenced by the interspecies scattering length and trap potentials so the interaction of spikes becomes complicated, and the locations of spikes are difficult to be determined. Here we study spikes of a double condensate by analyzing least energy (ground state) solutions of two-component systems of nonlinear Schrödinger equations with trap potentials. Our mathematical arguments may prove how trap potentials and the interspecies scattering length affect the locations of spikes. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.