Curvature computations for a two-component Camassa-Holm equation with vorticity

被引：0
|
作者：
Kohlmann, Martin [1 ]
机构：
[1] Tech Univ Carolo Wilhelmina Braunschweig, Braunschweig, Germany
来源：
APPLICABLE ANALYSIS | 2017年 / 96卷 / 02期
关键词：
Camassa-Holm equation; diffeomorphism group; geodesic flow; sectional curvature; 35Q35; 53C21; 53D25; 58B25; 58D05; BLOW-UP PHENOMENA; DEGASPERIS-PROCESI EQUATION; TRAVELING-WAVE SOLUTIONS; SHALLOW-WATER EQUATION; WELL-POSEDNESS; DIFFEOMORPHISM GROUP; GEOMETRY; SYSTEM; LIE;
D O I：
10.1080/00036811.2015.1134784
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, a two-component Camassa-Holm (2CH) system with vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims at presenting various details of the geometric formalism and a major result is the computation of the sectional curvature K of the underlying configuration manifold. As a further result, we show that there are directions for which K is strictly positive and bounded away from zero.
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页码：307 / 323
页数：17
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