We consider the initial-value problem for the one-dimensional nonlinear Schrödinger 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.
|Publication status||Published - Jul 3 2018|
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