Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach

TL;DR

This paper investigates the geometric properties and solution behaviors of a higher order two-component Camassa-Holm system with fractional inertia, establishing conditions for global existence and geodesic completeness.

Contribution

It introduces a geometric framework for analyzing higher order two-component Camassa-Holm systems with fractional inertia operators, including criteria for global solutions and geodesic completeness.

Findings

Criteria for global existence of solutions.

Flow is geodesically complete for inertia operators of order higher than three.

Analysis based on a geometric approach.

Abstract

In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.