Travelling wave solutions for some two-component shallow water models

Denys Dutykh, Delia Ionescu-Kruse

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In the present study we perform a unified analysis of travelling wave solutions to three different two-component systems which appear in shallow water theory. Namely, we analyze the celebrated Green-Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models. In particular, we show the existence of new type of solutions.

Original languageBritish English
Pages (from-to)1099-1114
Number of pages16
JournalJournal of Differential Equations
Volume261
Issue number2
DOIs
StatePublished - 15 Jul 2016

Keywords

  • Camassa-Holm equations
  • Cnoidal waves
  • Green-Naghdi model
  • Phase-plane analysis
  • Serre equations
  • Solitary waves
  • Travelling waves

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