2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57742We present a contact transformation of the generalized Hunter--Saxton equation to the Euler--Poisson equation with special values of the Ovsiannikov invariants. We also find the general solution for the generalized Hunter--Saxton equation.Mathematical PhysicsDifferential Geometry58H05; 58J70; 35A30Contact Equivalence of the Generalized Hunter - Saxton Equation and the Euler - Poisson Equationtext