Wave-Breaking and Peakons for a Modified Camassa-Holm Equation

Guilong Gui, Yue Liu, Peter J. Olver, Changzheng Qu

Research output: Contribution to journalArticlepeer-review

196 Scopus citations


In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail.

Original languageEnglish (US)
Pages (from-to)731-759
Number of pages29
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - May 2013


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