On a two-component π-Camassa-Holm system

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Kohlmann, Martin

关键词: Camassa-Holm equation;    Diffeomorphism group;    Semidirect product;    Geodesic flow;    Sectional curvature;    Well-posedness;   

DOI  :  10.1016/j.geomphys.2012.01.001

来源: Elsevier

【 摘 要 】

A novel pi-Camassa-Holm system is studied as a geodesic flow on a semidirect product obtained from the diffeomorphism group of the circle. We present the corresponding details of the geometric formalism for metric Euler equations on infinite-dimensional Lie groups and compare our results to what has already been obtained for the usual two-component Camassa-Holm equation. Our approach results in well-posedness theorems and explicit computations of the sectional curvature. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free