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 . In particular, we establish the asymptotic stability of the family of small solitary waves.

Keywords
NLS, solitary waves, asymptotic stability, delta potential
Mathematical Subject Classification 2010
Primary: 35Q55
Milestones
Received: 31 July 2018
Revised: 28 January 2019
Accepted: 18 April 2019
Published: 13 June 2020
Authors
Satoshi Masaki
Department of Systems Innovation
Graduate School of Engineering Science
Osaka University
Osaka
Japan
Jason Murphy
Department of Mathematics and Statistics
Missouri University of Science and Technology
Rolla, MO
United States
Jun-ichi Segata
Mathematical Institute
Tohoku University
Sendai
Japan