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

页码：313 / 322

页数：10

共 50 条

[1] Euler-Poincar, equations on semi-direct products
Cismas, Emanuel-Ciprian
MONATSHEFTE FUR MATHEMATIK, 2016, 179 (04): : 491 - 507
[2] Euler-Poincaré equations on semi-direct products
Emanuel-Ciprian Cismas
Monatshefte für Mathematik, 2016, 179 : 491 - 507
[3] Direct and Semi-Direct Product of Neutrosophic Extended Triplet Group
Shalla, Moges Mekonnen
Olgun, Necati
NEUTROSOPHIC SETS AND SYSTEMS, 2019, 29 : 197 - 214
[4] EULER-POINCARE-ARNOLD EQUATIONS ON SEMI-DIRECT PRODUCTS II
Cismas, Emanuel-Ciprian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (11) : 5993 - 6022
[5] SCHUR MULTIPLIER OF A SEMI-DIRECT PRODUCT
EVENS, L
ILLINOIS JOURNAL OF MATHEMATICS, 1972, 16 (01) : 166 - &
[6] REPRESENTATIONS OF A SEMI-DIRECT PRODUCT BY QUANTIZATION
RAWNSLEY, JH
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1975, 78 (SEP) : 345 - 350
[7] SEMI-DIRECT PRODUCT FOR INVERSE SEMIGROUPS
BATBEDAT, A
SEMIGROUP FORUM, 1979, 17 (04) : 283 - 305
[8] On semi-direct extensions of the Heisenberg group
Calvaruso, Giovanni
COLLECTANEA MATHEMATICA, 2021, 72 (01) : 1 - 23
[9] On semi-direct extensions of the Heisenberg group
Giovanni Calvaruso
Collectanea Mathematica, 2021, 72 : 1 - 23
[10] Covering a semi-direct product and intersective polynomials
Lee, Paul D.
Spearman, Blair K.
Yang, Qiduan
MANUSCRIPTA MATHEMATICA, 2016, 150 (3-4) : 521 - 531

← 1 2 3 4 5 →