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

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
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.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 3.236.13.53 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.