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

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

doi:10.1016/j.physd.2010.07.006

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	2050-2056
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	239
Issue number	23-24
DOIs	https://doi.org/10.1016/j.physd.2010.07.006
State	Published - 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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10.1016/j.physd.2010.07.006

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AB - 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.

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KW - Nonlinear partial differential equations

KW - RiemannHilbert analysis

KW - Scattering and inverse scattering theory

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

Abstract

Keywords

ASJC Scopus subject areas

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