Periodic Peakons and Compacton Families of the Hirota-Type Peakon Equation

In this paper, the methodologies of dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] are applied to find the solutions in the form of [Formula: see text] for the Hirota-type peakon equation posed by [Anco & Mobasheramini, 2017; Anco et al., 2021]. For the function [Formula: see text] therein, under the parameter conditions of [Formula: see text] [Formula: see text] or [Formula: see text], the existence of some possible bounded solutions (solitary wave solutions, periodic wave solutions and periodic peakons, as well as compactons) is proved, with exact explicit parametric representations obtained, except for the peakon solution.