Asymptotic Dynamics of Nonlinear Schrödinger Equations with Many Bound States

Details Asymptotic Dynamics of Nonlinear Schrödinger Equations with Many Bound States Asymptotic Dynamics of Nonlinear Schrödinger Equations with Many Bound States

2002-04-30

arxiv.org/abs/math-ph/0204056v1

Physics

Mathematical Physics

Scientific paper

We consider a nonlinear Schr\"odinger equation with a bounded local potential in $R^3$. 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 $H^1$, and that its ground state component is larger than $n^{3-\epsilon}$ with $\epsilon>0$ small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity.

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