Abstract:

First, I will briefly discuss a few applications where the nonlinear Schrodinger equations appears as a model. Second, I will discuss existence and uniqueness of initial value problems, existence of special solutions: solitons and bound states, and their role in the asymptotic behavior of problems with arbitrary initial data. At the end I will present open problems regarding the asymptotic completeness conjecture which states that any initial data evolves into a superposition of special solutions and a part that radiates to infinity.