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Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential. (English) Zbl 1443.81029

Summary: In this paper, we consider the nonlinear Schrödinger equation \(i \partial_t \psi = - \frac{1}{2} \Delta \psi + V(t, x) \psi - F(| \psi |^2) \psi\) with time-dependent potential in \(\mathbb{R}^3\). We prove that the weakly interacting \(N\)-soliton is asymptotically stable in a Sobolev space \(H^1(\mathbb{R}^3)\) under certain assumptions on the time dependent potential \(V(t, x)\) and the spectral structures of the linearized Hamiltonian.
©2020 American Institute of Physics

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
35C08 Soliton solutions
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
93B18 Linearizations
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