High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This article is devoted to the nonlinear Schrödinger equation [InlineMediaObject not available: see fulltext.] when the parameter ε approaches zero. All possible asymptotic behaviors of bounded solutions can be described by means of envelopes, or alternatively by adiabatic profiles. We prove that for every envelope, there exists a family of solutions reaching that asymptotic behavior, in the case of bounded intervals. We use a combination of the Nehari finite dimensional reduction together with degree theory. Our main contribution is to compute the degree of each cluster, which is a key piece of information in order to glue them.

Original languageEnglish
Pages (from-to)333-366
Number of pages34
JournalArchive for Rational Mechanics and Analysis
Volume182
Issue number2
DOIs
Publication statusPublished - 2006 Oct 1

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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