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.

引用

页码：307 / 323

页数：17

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