Algebraic Discretization of the CamassaHolm and HunterSaxton Equations
(2008) In Journal of Nonlinear Mathematical Physics 15. p.112 Abstract
 The CamassaHolm (CH) and HunterSaxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and. H1 rightinvariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a rightinvariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left invariant metric on SO(3). The CH and HS equations are integrable bihamiltonian equations and one of their Hamiltonian structures is associated to the Virasoro algebra. The parallel with the integrable SO(3) top is... (More)
 The CamassaHolm (CH) and HunterSaxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and. H1 rightinvariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a rightinvariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left invariant metric on SO(3). The CH and HS equations are integrable bihamiltonian equations and one of their Hamiltonian structures is associated to the Virasoro algebra. The parallel with the integrable SO(3) top is made explicit by a discretization of both equation based on Fourier modes expansion. The obtained equations represent integrable tops with infinitely many momentum components. An emphasis is given on the structure of the phase space of these equations, the momentum map and the space of canonical variables. (Less)
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http://lup.lub.lu.se/record/1375226
 author
 Ivanov, Rossen I ^{LU}
 organization
 publishing date
 2008
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Nonlinear Mathematical Physics
 volume
 15
 pages
 1  12
 publisher
 Bokförlaget Atlantis
 external identifiers

 wos:000263517200002
 scopus:51149105279
 ISSN
 14029251
 language
 English
 LU publication?
 yes
 id
 b62c130f16fb40c18e70f6d03cf97161 (old id 1375226)
 date added to LUP
 20090507 13:09:35
 date last changed
 20171022 04:15:18
@article{b62c130f16fb40c18e70f6d03cf97161, abstract = {The CamassaHolm (CH) and HunterSaxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and. H1 rightinvariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a rightinvariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left invariant metric on SO(3). The CH and HS equations are integrable bihamiltonian equations and one of their Hamiltonian structures is associated to the Virasoro algebra. The parallel with the integrable SO(3) top is made explicit by a discretization of both equation based on Fourier modes expansion. The obtained equations represent integrable tops with infinitely many momentum components. An emphasis is given on the structure of the phase space of these equations, the momentum map and the space of canonical variables.}, author = {Ivanov, Rossen I}, issn = {14029251}, language = {eng}, pages = {112}, publisher = {Bokförlaget Atlantis}, series = {Journal of Nonlinear Mathematical Physics}, title = {Algebraic Discretization of the CamassaHolm and HunterSaxton Equations}, volume = {15}, year = {2008}, }