Solitary wave solutions to the Isobe-Kakinuma model for water waves

Mathieu Colin, Tatsuo Iguchi

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of a flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show theoretically the existence of a family of small amplitude solitary wave solutions to the Isobe-Kakinuma model in the long wave regime. Numerical analysis for large amplitude solitary wave solutions is also provided and suggests the existence of a solitary wave of extreme form with a sharp crest.

Original languageEnglish
Pages (from-to)52-80
Number of pages29
JournalStudies in Applied Mathematics
Volume145
Issue number1
DOIs
Publication statusPublished - 2020 Jul 1

Keywords

  • fluid dynamics
  • nonlinear waves
  • partial differential equations
  • water waves

ASJC Scopus subject areas

  • Applied Mathematics

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