## 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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