Under investigation in this work is the Degasperis–Procesi equation with a strong dispersive term, which can be investigated as a model for shallow water dynamics. With the help of distribution theory, a direct and effective way is used to succinctly study the multi-peakon solutions of the equation. These multi-peakon solutions are obtained in weak sense. In particular, several types of double-peakon solutions are discussed in detail. Moreover, the dynamic behaviors the double-peakon solutions are illustrated through some figures.

中文翻译：

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具有强色散项的 Degasperis-Procesi 方程及其多峰解

这项工作正在研究的是具有强色散项的 Degasperis-Procesi 方程，可以将其作为浅水动力学模型进行研究。借助分布理论，用一种直接有效的方法来简洁地研究方程的多峰解。这些多峰解是在弱意义下获得的。特别地，详细讨论了几种类型的双峰解决方案。此外，通过一些图形说明了双峰解的动态行为。