2022•SymmetryOpen access

Exact Traveling Wave Solutions in a Generalized Harry Dym Type Equation

Rong Wu, Yan Zhou

Abstract

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions in parameter space are examined. It is demonstrated that solitary wave solutions, periodic peakons, pseudo-peakons, and compacton solutions exist. All conceivable exact explicit parametric representations of various solutions are presented.

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Key concepts: Traveling wave, Periodic wave, Type (biology), Parametric statistics, Mathematical analysis, Space (punctuation), Parameter space, Dynamical systems theory