Euler equations on a semi-direct product of the diffeomorphisms group by itself

Joachim Escher; Rossen Ivanov; Boris Kolev

doi:10.3934/jgm.2011.3.313

Euler equations on a semi-direct product of the diffeomorphisms group by itself

Joachim Escher, Rossen Ivanov, Boris Kolev

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S ¹)sDiff(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) sVect(S ¹))* are found.

Original language	English
Pages (from-to)	313-322
Number of pages	10
Journal	Journal of Geometric Mechanics
Volume	3
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2011.3.313 https://doi.org/10.21427/e77w-0z73
Publication status	Published - Sep 2011

Keywords

Dieomorphism group of the circle
Euler equation
Integrable systems
Peakons

Access to Document

10.3934/jgm.2011.3.313
10.21427/e77w-0z73Licence: CC BY-NC-SA

Cite this

@article{f8e4846564d54016af323b73a907716d,

title = "Euler equations on a semi-direct product of the diffeomorphisms group by itself",

abstract = "The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(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) sVect(S 1))* are found.",

keywords = "Dieomorphism group of the circle, Euler equation, Integrable systems, Peakons",

author = "Joachim Escher and Rossen Ivanov and Boris Kolev",

year = "2011",

month = sep,

doi = "10.3934/jgm.2011.3.313",

language = "English",

volume = "3",

pages = "313--322",

journal = "Journal of Geometric Mechanics",

issn = "1941-4889",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - Euler equations on a semi-direct product of the diffeomorphisms group by itself

AU - Escher, Joachim

AU - Ivanov, Rossen

AU - Kolev, Boris

PY - 2011/9

Y1 - 2011/9

N2 - The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(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) sVect(S 1))* are found.

AB - The geodesic equations of a class of right invariant metrics on the semi-direct product Diff(S 1)sDiff(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) sVect(S 1))* are found.

KW - Dieomorphism group of the circle

KW - Euler equation

KW - Integrable systems

KW - Peakons

UR - https://www.scopus.com/pages/publications/84866426517

U2 - 10.3934/jgm.2011.3.313

DO - 10.3934/jgm.2011.3.313

M3 - Article

AN - SCOPUS:84866426517

SN - 1941-4889

VL - 3

SP - 313

EP - 322

JO - Journal of Geometric Mechanics

JF - Journal of Geometric Mechanics

IS - 3

ER -

Euler equations on a semi-direct product of the diffeomorphisms group by itself

Abstract

Keywords

Access to Document

Fingerprint

Cite this