Explicit solutions of the Camassa-Holm equation

E.J. Parkes, V.O. Vakhnenko

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1309-1316
Number of pages7
JournalChaos, Solitons and Fractals
Issue number5
Publication statusPublished - Dec 2005


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


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