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Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations. (English) Zbl 1067.35113

This paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation of the form \(i \psi_t = - \triangle \psi + F(| \psi| ^2) \psi\), where \(F\) is some smooth function. It is assumed that \(\psi\) is a function of \((t,x) \in \mathbb R \times \mathbb R^d\) with \(d \geq 3\) and that the initial solution is close to a sum of \(N\) decoupled solitons. Under certain assumptions on the spectral structure of the one soliton linearizations, the author proves that for a large value of the time variable \(t\) the asymptotic solution is given by a sum of solitons with slightly modified parameters and a small dispersive term.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35K45 Initial value problems for second-order parabolic systems
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