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

journal contribution
posted on 2023-06-08, 17:20 authored by E Kirr, A Zarnescu
We consider the cubic nonlinear Schrödinger 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.

History

Publication status

  • Published

Journal

Communications in Mathematical Physics

ISSN

0010-3616

Publisher

Springer Verlag

Issue

2

Volume

272

Page range

443-468

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-05-18

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