We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics