Asymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance Dominated and Radiation Dominated Solutions

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dc.creatorTsai, Tai-Peng
dc.creatorYau, Horng-Tzer
dc.date2000-11-22
dc.date2001-02-05
dc.date.accessioned2026-07-07T04:28:08Z
dc.date.available2026-07-07T04:28:08Z
dc.descriptionWe consider a linear Schrödinger equation with a small nonlinear perturbation in $R^3$. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the initial data is near a nonlinear ground state, then the solution approaches to certain nonlinear ground state as the time tends to infinity. Furthermore, the difference between the wave function solving the nonlinear Schrödinger equation and its asymptotic profile can have two different types of decay: 1. The resonance dominated solutions decay as $t^{-1/2}$. 2. The radiation dominated solutions decay at least like $t^{-3/2}$.
dc.descriptionlatex, 71 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0011036
dc.identifierhttp://arxiv.org/abs/math-ph/0011036
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56672
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.titleAsymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance Dominated and Radiation Dominated Solutions
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