## Asymptotic dynamics of nonlinear Schrödinger equations with many bound states.(English)Zbl 1038.35128

The author considers a nonlinear Schrödinger equation with a smooth localized real potential $$V$$, $$i\partial_t\psi=(-\Delta+V)\psi+\lambda | \psi| ^2\psi$$, where $$-\Delta+V$$ is assumed to have three or more bound states. It is shown, under certain conditions on the initial data, that the solution will converge locally to a nonlinear ground state. This extends the author’s previous work with H.-T. Yau [Commun. Pure Appl. Math. 55, 153–216 (2002; Zbl 1031.35137), Int. Math. Res. Notes 31, 1629–1673 (2002; Zbl 1011.35120)].

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q40 PDEs in connection with quantum mechanics 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

### Citations:

Zbl 1031.35137; Zbl 1011.35120
Full Text:

### References:

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