The Journal of Geometric Mechanics (JGM)

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

Pages: 281 - 293, Volume 7, Issue 3, September 2015      doi:10.3934/jgm.2015.7.281

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Joachim Escher - Institute for Applied Mathematics, University of Hanover, D-30167 Hanover, Germany (email)
Tony Lyons - School of Mathematical Sciences, University College Cork, Cork, Ireland (email)

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.

Keywords:  Diffeomorphism group, geodesic flow, global solutions.
Mathematics Subject Classification:  22E65, 58D05, 35Q53.

Received: March 2015;      Revised: June 2015;      Available Online: July 2015.