Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation

Satoshi Masaki, Jun ichi Segata

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆr space where Lˆr={f∈S(R)|‖f‖r=‖fˆ‖Lr<∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)283-326
Number of pages44
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume35
Issue number2
DOIs
Publication statusPublished - 2018 Mar

Keywords

  • Generalized Korteweg–de Vries equation
  • Scattering problem
  • Threshold solution

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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