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On asymptotic stability of solitons in a nonlinear Schrödinger equation

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  • The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator through a localized nonlinearity. The coupled system is $U(1)$ invariant. This article, which extends the results of a previous one, provides a proof of asymptotic stability of the solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
    Mathematics Subject Classification: 35Q55, 37K40.


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