RESEARCH ARTICLE

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

  • Zhijun QIAO , 1 ,
  • Baoqiang XIA 1,2
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  • 1. Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541, USA
  • 2. School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China

Received date: 18 Apr 2013

Accepted date: 03 Jun 2013

Published date: 01 Oct 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Zhijun QIAO , Baoqiang XIA . Integrable peakon systems with weak kink and kink-peakon interactional solutions[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1185 -1196 . DOI: 10.1007/s11464-013-0314-x

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