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On asymptotic stability of solitons in a nonlinear Schrödinger equation

Abstract Related Papers Cited by
  • 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.

    Citation:

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  • [1]

    V. Buslaev, A. Komech, E. Kopylova and D. Stuart, On asymptotic stability of solitary waves in a nonlinear Schrödinger equation, Comm. Partial Diff. Eqns., \textbf{33} (2008), 669-705.doi: 10.1080/03605300801970937.

    [2]

    V. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 20 (2003), 419-475.doi: 10.1016/S0294-1449(02)00018-5.

    [3]

    A. I. Komech and A. A. Komech, Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator, Russ. J. Math. Phys., 14 (2007), 164-173.doi: 10.1134/S1061920807020057.

    [4]

    A. Komech and E.Kopylova, On Asymptotic stability of moving kink for relativistic Ginsburg-Landau equation, Commun. Math. Phys., 302 (2011), 225-252.doi: 10.1007/s00220-010-1184-7.

    [5]

    A. Komech, E. Kopylova and D. StuartOn asymptotic stability of solitons for nonlinear Schrödinger equation, preprint, arXiv:0807.1878.

    [6]

    M. Merkli and I. M. Sigal, A time-dependent theory of quantum resonances, Commun. Math. Phys., 201 (1999), 549-576.doi: 10.1007/s002200050568.

    [7]

    R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Commun. Math. Phys., 164 (1994), 305-349.doi: 10.1007/BF02101705.

    [8]

    C. A. Pillet and C. E. Wayne, Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, J. Diff. Eqns, 141 (1997), 310-326.doi: 10.1006/jdeq1997.3345.

    [9]

    A. Soffer and M. I. Weinstein, Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math., 136 (1999), 9-74.doi: 10.1007/s002220050303.

    [10]

    A. Soffer and M. I. Weinstein, Selection of the ground state for nonlinear Schrodinger equations, Rev. Math. Phys., 16 (2004), 977-1071.doi: 10.1142/S0129055X04002175.

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