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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 ZarnescuWe 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.
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Publication status
- Published
Journal
Communications in Mathematical PhysicsISSN
0010-3616Publisher
Springer VerlagExternal DOI
Issue
2Volume
272Page range
443-468Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2014-05-18Usage metrics
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