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

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Guilong Gui, Yue Liu, Peter J Olver, Changzheng Qu

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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.

This article was published in Communications in Mathematical Physics and referenced in Journal of Generalized Lie Theory and Applications

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