EULER EQUATIONS ON A SEMI-DIRECT PRODUCT OF THE DIFFEOMORPHISMS GROUP BY ITSELF

被引：11
|
作者：
Escher, Joachim [1 ]
Ivanov, Rossen [2 ]
Kolev, Boris [3 ,4 ]
机构：
[1] Leibniz Univ Hannover, Inst Appl Math, D-30167 Hannover, Germany
[2] Dublin Inst Technol, Sch Math Sci, Dublin 8, Ireland
[3] Univ Aix Marseille 1, F-13453 Marseille 13, France
[4] CNRS, LATP, F-13453 Marseille 13, France
来源：
JOURNAL OF GEOMETRIC MECHANICS | 2011年 / 3卷 / 03期
基金：
爱尔兰科学基金会;
关键词：
Euler equation; integrable systems; peakons; diffeomorphism group of the circle; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; GEOMETRIC APPROACH; BREAKING WAVES; GEODESIC-FLOW; CIRCLE; INTEGRABILITY; SYSTEMS; LIE;
D O I：
10.3934/jgm.2011.3.313
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S(1))(S)Diff (S(1)) are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra (Vect(S(1))(S)Vect(S(1)))* are found.
引用
收藏
页码：313 / 322
页数：10
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