On a two-component π-Camassa-Holm system

被引：13
作者：
Kohlmann, Martin [1 ]
机构：
[1] Tech Univ Carolo Wilhelmina Braunschweig, Peter L Reichertz Inst Med Informat, D-38106 Braunschweig, Germany
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2012年 / 62卷 / 04期
关键词：
Camassa-Holm equation; Diffeomorphism group; Semidirect product; Geodesic flow; Sectional curvature; Well-posedness; SHALLOW-WATER EQUATION; DIFFEOMORPHISM GROUP; GEODESIC-FLOW; WELL-POSEDNESS; LIE-GROUPS; GEOMETRY; CIRCLE; SOLITONS; MOTION;
D O I：
10.1016/j.geomphys.2012.01.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：832 / 838
页数：7
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