Global existence of small solutions to a relativistic nonlinear Schrödinger equation

Anne De Bouard, Nakao Hayashi, Jean Claude Saut

Research output: Contribution to journalArticlepeer-review

150 Citations (Scopus)

Abstract

We study the Cauchy problem associated to a nonlinear Schrödinger equation modelling the self-channeling of a high power, ultra-short laser pulse in matter. The new nonlinear terms arise from relativistic effects and from the ponderomotive force. We prove global existence and uniqueness of small solutions in transverse space dimensions 2 and 3, and local existence without any smallness condition in transverse space dimension 1.

Original languageEnglish
Pages (from-to)73-105
Number of pages33
JournalCommunications in Mathematical Physics
Volume189
Issue number1
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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