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On small energy stabilization in the NLS with a trapping potential. (English) Zbl 1326.35335

Summary: We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential, generalizing work of A. Soffer and M. I. Weinstein [Rev. Math. Phys. 16, No. 8, 977–1071 (2004; Zbl 1111.81313)], and of Tsai and Yau. The novelty is that we allow generic spectra associated to the potential. This is a new application of the idea of interpreting the nonlinear Fermi golden rule as a consequence of the Hamiltonian structure.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs

Citations:

Zbl 1111.81313
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