Asymptotic dynamics of nonlinear Schrödinger equations with many bound states |
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Authors: | Tai-Peng Tsai |
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Affiliation: | School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA |
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Abstract: | We consider a nonlinear Schrödinger equation with a bounded localized potential in . The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H1, and that its ground state component is larger than n3−ε with ε>0 small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity. |
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Keywords: | Primary 35Q40 35Q55 |
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