On Asymptotic Stability of Solitary Waves in Discrete Schrödinger Equation Coupled to Nonlinear Oscillator
نویسنده
چکیده
The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete 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 [2]: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection, method of majorants, etc. Supported partly by FWF grant P19138-N13, DFG grant 436 RUS 113/929/0-1 and RFBR grant 07-0100018a.
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