Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data

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)5505-5624
Number of pages120
JournalInternational Mathematics Research Notices
Volume2011
Issue number24
DOIs
StatePublished - 2011

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Long-time Asymptotics
Nonlinear Equations
Half line
Steepest Descent Method
Robin Boundary Conditions
Riemann-Hilbert Problem
Boundary Problem
Soliton Solution
Asymptotic Stability
Perturbation
Line

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data. / Deift, Percy; Park, Jungwoon.

In: International Mathematics Research Notices, Vol. 2011, No. 24, 2011, p. 5505-5624.

Research output: Contribution to journalArticle

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