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

Satoshi Masaki, Jason Murphy, Jun Ichi Segata

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the initial-value problem for the one-dimensional nonlinear Schrodinger 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.

Original languageEnglish
Pages (from-to)1099-1128
Number of pages30
JournalAnalysis and PDE
Volume13
Issue number4
DOIs
Publication statusPublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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