Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data: Announcement of Results

Percy Deift, Jungwoon Park

Research output: Contribution to journalArticle

Abstract

We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a Bäcklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, the earlier work on the problem by Holmer and Zworski.

Original languageEnglish (US)
Pages (from-to)143-156
Number of pages14
JournalLetters in Mathematical Physics
Volume96
Issue number1-3
DOIs
StatePublished - Jun 1 2011

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Keywords

  • Riemann-Hilbert problem
  • initial-boundary value problem
  • long-time behavior
  • nonlinear Schrödinger equation
  • nonlinear steepest descent

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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