TL;DR
This paper explores a Whitham-type equation, showing that the Hunter-Saxton equation and the Gurevich-Zybin system are two non-equivalent forms of it, and derives all their common solutions explicitly.
Contribution
It establishes the equivalence of two different representations of a Whitham-type equation and finds their shared solutions exactly.
Findings
Hunter-Saxton and Gurevich-Zybin are non-equivalent forms of the same equation.
All common solutions of these forms are obtained explicitly.
The work provides a complete characterization of their shared solutions.
Abstract
The Hunter-Saxton equation and the Gurevich-Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained exactly.
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