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 u (x , t) = ϕ (x − c t) e i (κ x − ω t) for the Hirota-type peakon equation posed by [Anco & Mobasheramini, 2017; Anco et al., 2021]. For the function ϕ (ξ) therein, under the parameter conditions of κ = 5 3 , c = 8 0 7 ω 1 0 0 or c ≠ 8 0 7 ω 1 0 0 , 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. [ABSTRACT FROM AUTHOR]