An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

Yasuhiro Ohta, Ken Ichi Maruno, Bao Feng Feng

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

An integrable semi-discretization of the Camassa-Holm (CH) equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

Original languageEnglish
Article number355205
JournalJournal of Physics A: Mathematical and Theoretical
Volume41
Issue number35
DOIs
Publication statusPublished - 2008 Sep 5
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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