Asymptotic dynamics of nonlinear Schrödinger equations with many bound states

AbstractWe consider a nonlinear Schrödinger equation with a bounded localized potential in R3. The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H1, and that its ground state component is larger than n3−ε with ε>0 small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity