On Asymptotic Stability of Solitary Waves in a Nonlinear Schrödinger Equation
نویسندگان
چکیده
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 manifold, the symplectic orthogonal projection and method of majorants. 1 Supported partly by RFBR research grants 05-0101076 and 05-01002944. 2 On leave Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia. Supported partly by FWF grant P19138-N13 and Max-Planck Institute for Mathematics in the Sciences (Leipzig). Supported partly by FWF grant P19138-N13 and RFBR grant 06-01-00096. Partially supported by EPSRC grant A00133/01
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