On the asymptotic stability of bound states in 2D cubic Schroedinger equation

Details On the asymptotic stability of bound states in 2D cubic Schroedinger equation On the asymptotic stability of bound states in 2D cubic Schroedinger equation

2006-03-23

arxiv.org/abs/math/0603550v1

Mathematics

Analysis of PDEs

27 pages; references added

Scientific paper

We consider the cubic nonlinear Schr\"{o}dinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space initial data, converge to the set of bound states. Therefore, the center manifold in this problem is a global attractor. The proof hinges on dispersive estimates that we obtain for the non-autonomous, non-Hamiltonian, linearized dynamics around the bound states.

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