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

Patricio Felmer*, Salomé Martínez, Kazunaga Tanaka

*この研究の対応する著者

研究成果: Article査読

11 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)333-366
ページ数34
ジャーナルArchive for Rational Mechanics and Analysis
182
2
DOI
出版ステータスPublished - 2006 10月

ASJC Scopus subject areas

  • 分析
  • 数学(その他)
  • 機械工学

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