On Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation

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dc.creatorBuslaev, V.
dc.creatorKomech, A.
dc.creatorKopylova, E.
dc.creatorStuart, D.
dc.date2007-02-04
dc.date.accessioned2026-07-07T07:44:43Z
dc.date.available2026-07-07T07:44:43Z
dc.descriptionThe long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. The proofs use the strategy of Buslaev-Perelman: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection and method of majorants.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0702013
dc.identifierhttp://arxiv.org/abs/math-ph/0702013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123300
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject37K; 35B41; 35L; 35Q; 35P25; 81
dc.titleOn Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation
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