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2020 Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
Anal. PDE 13(4): 1099-1128 (2020). DOI: 10.2140/apde.2020.13.1099

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.

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Satoshi Masaki. Jason Murphy. Jun-ichi Segata. "Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential." Anal. PDE 13 (4) 1099 - 1128, 2020. https://doi.org/10.2140/apde.2020.13.1099

Information

Received: 31 July 2018; Revised: 28 January 2019; Accepted: 18 April 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07221198
MathSciNet: MR4109901
Digital Object Identifier: 10.2140/apde.2020.13.1099

Subjects:
Primary: 35Q55

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2020
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