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Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions

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Abstract

This paper is devoted to a new integrable two-component Camassa–Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable system that admits weak kink and kink–peakon interactional solutions. In addition, the new system includes both standard (quadratic) and cubic Camassa–Holm equations as two special cases. In the paper, we first establish the local well-posedness for the Cauchy problem of the system, and then derive a precise blow-up scenario and a new blow-up result for strong solutions to the system with both quadratic and cubic nonlinearity. Furthermore, its peakon and weak kink solutions are discussed as well.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong, China

    Kai Yan & Zhaoyang Yin

  2. Department of Mathematics, University of Texas-Pan American, Edinburg, TX, 78541, USA

    Zhijun Qiao

  3. Faculty of Information Technology, Macau University of Science and Technology, Macau, China

    Zhaoyang Yin

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  1. Kai Yan
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  2. Zhijun Qiao
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  3. Zhaoyang Yin
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Correspondence to Zhijun Qiao.

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Communicated by P. Deift

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Yan, K., Qiao, Z. & Yin, Z. Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions. Commun. Math. Phys. 336, 581–617 (2015). https://doi.org/10.1007/s00220-014-2236-1

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