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Remarks on the Lagrangian representation of bi-Hamiltonian equations. / Pavlov, M. V.; Vitolo, R. F.

In: Journal of Geometry and Physics, Vol. 113, 01.03.2017, p. 239-249.

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

Harvard

Pavlov, MV & Vitolo, RF 2017, 'Remarks on the Lagrangian representation of bi-Hamiltonian equations', Journal of Geometry and Physics, vol. 113, pp. 239-249. https://doi.org/10.1016/j.geomphys.2016.10.013

APA

Pavlov, M. V., & Vitolo, R. F. (2017). Remarks on the Lagrangian representation of bi-Hamiltonian equations. Journal of Geometry and Physics, 113, 239-249. https://doi.org/10.1016/j.geomphys.2016.10.013

Vancouver

Pavlov MV, Vitolo RF. Remarks on the Lagrangian representation of bi-Hamiltonian equations. Journal of Geometry and Physics. 2017 Mar 1;113:239-249. doi: 10.1016/j.geomphys.2016.10.013

Author

Pavlov, M. V. ; Vitolo, R. F. / Remarks on the Lagrangian representation of bi-Hamiltonian equations. In: Journal of Geometry and Physics. 2017 ; Vol. 113. pp. 239-249.

BibTeX

@article{fa51efb843864f5184abb52d9ef5616f,
title = "Remarks on the Lagrangian representation of bi-Hamiltonian equations",
abstract = "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.",
keywords = "Bi-Hamiltonian structure, Hydrodynamic type system, Lagrangian representation, WDVV equations, WDW equations, TOPOLOGICAL FIELD-THEORY, POISSON BRACKETS, HYDRODYNAMIC-TYPE, INTEGRABLE SYSTEMS, 3RD-ORDER, WDVV EQUATIONS, MANIFOLDS, OPERATORS, ASSOCIATIVITY, GEOMETRY",
author = "Pavlov, {M. V.} and Vitolo, {R. F.}",
note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2017",
month = mar,
day = "1",
doi = "10.1016/j.geomphys.2016.10.013",
language = "English",
volume = "113",
pages = "239--249",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier",

}

RIS

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