Nonlinear Schrödinger systems with large interaction forces between different components

There have been many studies on the asymptotic behavior of low energy solutions for a single elliptic equation as an involved parameter approaches to a threshold. In this case, the asymptotic behavior depends on a balance between the differential operator and nonlinearity, and their interaction with a geometry of a underlying domain. On the other hand, even though the elliptic systems coming from nonlinear Schrödinger systems have a simple looking interaction terms, even the construction of nontrivial low energy solutions is not easy in general since the Morse indices of the nontrivial solutions could be high depending types of interaction terms. When the interaction forces between different components are very large, we believe that a relatively simpler structure we can see.Nevertheless, a wide variety of their asymptotic behavior we could imagine as various kinds of combination for the interaction between components might produce various effects on the asymptotic behavior.The general study for elliptic systems with large interaction forces is quite challenging. In this talk, I would like to introduce my recent studies with collaborators on three components systems as basic steps to get general understanding for elliptic systems with large interaction forces.