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

• DOI: 10.1007/s00220-012-1566-0
• Publication Date: 2012-09-10T06:32:22Z
• Authors: Guilong Gui; Yue Liu; Peter J. Olver; Changzheng Qu
• Keywords: Peakon; Camassa–Holm Equation

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.