Relaxation of Excited States in Nonlinear Schrödinger Equations

2001/10/08 by Tai-Peng Tsai, Horng-Tzer Yau, Tsai, Tai-Peng +1
Mathematics · Physics and Astronomy · #35Q40 #35Q55 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q40 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.math-ph/0110009

Submitted on August 27, 2001

arxiv created 2001/10/08 · arxiv updated 2009/11/30

Abstract

We consider a nonlinear Schrödinger equation in \R³ with a bounded local potential. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial data is small and is near some nonlinear \it excited state. We give a sufficient condition on the initial data so that the solution to the nonlinear Schrödinger equation approaches to certain nonlinear \it ground state as the time tends to infinity.

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