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

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.

Key words： Integrable system; Lax pair; peakon; weak kink; kink-peakon

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