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

Joachim Escher; Tony  Lyons

doi:10.3934/jgm.2015.7.281

Article Contents

2015, Volume 7, Issue 3: 281-293. Doi: 10.3934/jgm.2015.7.281

This issue Previous Article Hypersymplectic structures on Courant algebroids Next Article Lie algebroids generated by cohomology operators

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

Joachim Escher^1, and
Tony Lyons^2,

1.
Institute for Applied Mathematics, University of Hanover, D-30167 Hanover
2.
School of Mathematical Sciences, University College Cork, Cork

Received: February 28, 2015

Revised: May 31, 2015

Published: August 2015

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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.

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Mathematics Subject Classification: 22E65, 58D05, 35Q53.

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