On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow

Jun ichi Segata

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as "Hirota" equation. This equation is a mixture of cubic nonlinear Schrödinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given "modified" free profile by using the two asymptotic formulae for some oscillatory integrals.

Original languageEnglish
Pages (from-to)281-306
Number of pages26
JournalJournal of Differential Equations
Volume245
Issue number2
DOIs
Publication statusPublished - 2008 Jul 15

Keywords

  • Hirota equation
  • Large time asymptotics
  • Long range interaction

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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