Explicit solutions of the Camassa-Holm equation

E.J. Parkes, V.O. Vakhnenko

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Explicit travelling-wave solutions of the Camassa-Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis-Procesi equation are given in an appendix.
LanguageEnglish
Pages1309-1316
Number of pages7
JournalChaos, Solitons and Fractals
Volume26
Issue number5
DOIs
Publication statusPublished - Dec 2005

Fingerprint

x direction
Camassa-Holm Equation
Explicit Solution
Degasperis-Procesi Equation
Propagation
Peakon
Traveling Wave Solutions
Two Parameters
Mirror
Composite

Keywords

  • Camassa–Holm equation
  • solitons
  • finite element analysis
  • numerical mathematics

Cite this

Parkes, E.J. ; Vakhnenko, V.O. / Explicit solutions of the Camassa-Holm equation. In: Chaos, Solitons and Fractals. 2005 ; Vol. 26, No. 5. pp. 1309-1316.
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Explicit solutions of the Camassa-Holm equation. / Parkes, E.J.; Vakhnenko, V.O.

In: Chaos, Solitons and Fractals, Vol. 26, No. 5, 12.2005, p. 1309-1316.

Research output: Contribution to journalArticle

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