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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Jiangsu University, Zhenjiang, 212013, P.R. China

    Guilong Gui

  2. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Guilong Gui

  3. Department of Mathematics, University of Texas, Arlington, TX, 76019-0408, USA

    Yue Liu

  4. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Peter J. Olver

  5. Department of Mathematics, Ningbo University, Ningbo, 315211, P.R. China

    Changzheng Qu

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  1. Guilong Gui
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  2. Yue Liu
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  3. Peter J. Olver
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  4. Changzheng Qu
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Corresponding author

Correspondence to Peter J. Olver.

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Communicated by P. Constantin

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Gui, G., Liu, Y., Olver, P.J. et al. Wave-Breaking and Peakons for a Modified Camassa–Holm Equation. Commun. Math. Phys. 319, 731–759 (2013). https://doi.org/10.1007/s00220-012-1566-0

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  • DOI: https://doi.org/10.1007/s00220-012-1566-0

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