2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123300The 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: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection and method of majorants.35 pagesMathematical PhysicsAnalysis of PDEs37K; 35B41; 35L; 35Q; 35P25; 81text