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Remarks on the Lagrangian representation of bi-Hamiltonian equations. / Pavlov, M. V.; Vitolo, R. F.
в: Journal of Geometry and Physics, Том 113, 01.03.2017, стр. 239-249.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Remarks on the Lagrangian representation of bi-Hamiltonian equations
AU - Pavlov, M. V.
AU - Vitolo, R. F.
N1 - Publisher Copyright: © 2016 Elsevier B.V.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2=LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
AB - The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2=LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
KW - Bi-Hamiltonian structure
KW - Hydrodynamic type system
KW - Lagrangian representation
KW - WDVV equations
KW - WDW equations
KW - TOPOLOGICAL FIELD-THEORY
KW - POISSON BRACKETS
KW - HYDRODYNAMIC-TYPE
KW - INTEGRABLE SYSTEMS
KW - 3RD-ORDER
KW - WDVV EQUATIONS
KW - MANIFOLDS
KW - OPERATORS
KW - ASSOCIATIVITY
KW - GEOMETRY
UR - http://www.scopus.com/inward/record.url?scp=85007002950&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2016.10.013
DO - 10.1016/j.geomphys.2016.10.013
M3 - Article
AN - SCOPUS:85007002950
VL - 113
SP - 239
EP - 249
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
SN - 0393-0440
ER -
ID: 10064226