Solutions to the nonlinear Schrödinger equation with sequences of initial data converging to a Dirac mass

J. P. Newport, K. D.T.R. McLaughlin

Research output: Contribution to journalArticle

Abstract

We study the nonlinear Schrdinger equation with sequences of initial data that converge to a Dirac mass, and study the asymptotic behaviour of solutions. In doing so we find a connection to previously known long time asymptotics. We demonstrate a type of universality in the behaviour of solutions for real initial data, and we also show how this universality breaks down for examples of initial data that are not purely real.

Original languageEnglish (US)
Pages (from-to)2050-2056
Number of pages7
JournalPhysica D: Nonlinear Phenomena
Volume239
Issue number23-24
DOIs
StatePublished - Nov 1 2010

Keywords

  • Integrable systems
  • Nonlinear partial differential equations
  • RiemannHilbert analysis
  • Scattering and inverse scattering theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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