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Integrable peakon systems with weak kink and kink-peakon interactional solutions

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Abstract

We report two integrable peakon systems that have weak kink and kink-peakon interactional solutions. Both peakon systems are guaranteed integrable through providing their Lax pairs. The peakon and multi-peakon solutions of both equations are studied. In particular, the two-peakon dynamic systems are explicitly presented and their collisions are investigated. The weak kink solution is studied, and more interesting, the kink-peakon interactional solutions are proposed for the first time.

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Authors and Affiliations

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

    Zhijun Qiao & Baoqiang Xia

  2. School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, 221116, China

    Baoqiang Xia

Authors
  1. Zhijun Qiao
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  2. Baoqiang Xia
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Correspondence to Zhijun Qiao.

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Qiao, Z., Xia, B. Integrable peakon systems with weak kink and kink-peakon interactional solutions. Front. Math. China 8, 1185–1196 (2013). https://doi.org/10.1007/s11464-013-0314-x

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  • DOI: https://doi.org/10.1007/s11464-013-0314-x

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