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.


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