#### Vol. 13, No. 4, 2020

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Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential

### Satoshi Masaki, Jason Murphy and Jun-ichi Segata

Vol. 13 (2020), No. 4, 1099–1128
##### Abstract

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 $t\to \infty$. In particular, we establish the asymptotic stability of the family of small solitary waves.

##### Keywords
NLS, solitary waves, asymptotic stability, delta potential
Primary: 35Q55