On Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation

  title={On Asymptotic Stability of Solitary Waves in a Nonlinear Schr{\"o}dinger Equation},
  author={Vladimir S. Buslaev and A. I. Komech and Elena A. Kopylova},
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. The proofs use the strategy of Buslaev-Perelman [3, 4]: the linerization of the dynamics on the solitary… CONTINUE READING
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