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Nonlinear scattering: The states which are close to a soliton. (Russian. English summary) Zbl 0799.35197

Zap. Nauchn. Semin. POMI 200, 38-50, 70 (1992).
Summary: It is assumed that a nonlinear Schrödinger equation with general nonlinearity admits solutions of soliton type. The Cauchy problem with initial datum which is close to a soliton is considered. It is also assumed that the linearization of the equation on the soliton possesses only a real spectrum. The main result claims that the asymptotic behavior of the solution as \(t\to +\infty\) is given by the sum of a soliton with deformed parameters and a dispersive tail, i.e. a solution of the linear Schrödinger equation. In the previous work the case of the minimal spectrum is considered.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35P25 Scattering theory for PDEs
81U05 \(2\)-body potential quantum scattering theory
35Q51 Soliton equations
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