Concentration of solutions to a system of nonlinear Schrödinger equations*

Abstract: We consider a system of nonlinear elliptic equations that emerges as a model in various physical phenomena, for example, in the study of standing waves for a mixture of Bose-Einstein condensates of $\textit{m}$ hyperfine states that overlap in space. In the competitive case, that is, when the interaction between particles in the same state is attractive and the interaction between particles in two different states is repulsive, it happens that, by increasing the repulsive forces, the condensates separate spatially. This phenomenon is called phase separation and has been extensively studied. In this talk we will describe the behavior of the system when we simultaneously increase the attractive and repulsive forces. We will see that in this case a concentration phenomenon is produced, and we will analyze the limit profiles of solutions having positive and sign-changing components. This is joint work with Mayra Soares (postdoctoral fellow at UNAM).

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