On the classical solutions for the high order Camassa-Holm type equations

The high order Camassa-Holm equation describes the evolution of shallow water waves and the manifold of the smooth orientation-preserving diffeomorphisms of the unit circle in the plane S1. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem associated with these equations.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the evolution of shallow water waves described by the high order Camassa-Holm equation and the manifold of smooth orientation-preserving diffeomorphisms of the unit circle in the plane S1. The well-posedness of classical solutions for the Cauchy problem associated with these equations is proven.