A trihamiltonian extension of the Toda lattice

Chiara Andrà; Luca Degiovanni; Guido Magnano

doi:10.1016/j.geomphys.2006.06.008

A trihamiltonian extension of the Toda lattice

Chiara Andrà
, Luca Degiovanni
, Guido Magnano

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

Abstract

A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H of n × n Hermitian matrices. The new Poisson structure is of Lie-Poisson type with respect to the standard Lie bracket of H. This Poisson structure (together with two already known ones, obtained through a r-matrix technique) allows to construct an extension of the periodic Toda lattice with n particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given.

Original language	English
Pages (from-to)	863-880
Number of pages	18
Journal	Journal of Geometry and Physics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1016/j.geomphys.2006.06.008
Publication status	Published - Feb 2007
Externally published	Yes

Keywords

Classical integrable systems
Classical r-matrix
Periodic Toda lattice
Symplectic geometry
Trihamiltonian systems

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10.1016/j.geomphys.2006.06.008

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title = "A trihamiltonian extension of the Toda lattice",

abstract = "A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H of n × n Hermitian matrices. The new Poisson structure is of Lie-Poisson type with respect to the standard Lie bracket of H. This Poisson structure (together with two already known ones, obtained through a r-matrix technique) allows to construct an extension of the periodic Toda lattice with n particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given.",

keywords = "Classical integrable systems, Classical r-matrix, Periodic Toda lattice, Symplectic geometry, Trihamiltonian systems",

author = "Chiara Andr{\`a} and Luca Degiovanni and Guido Magnano",

note = "Funding Information: The authors are indebted with the anonymous referee for suggesting the relation between the Lie bracket and Hermitian matrices, which allowed a remarkable simplification of the whole construction. The work for this paper was partially supported by the PRIN research project “Geometric methods in the theory of nonlinear waves and their applications” of the Italian MIUR. ",

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T1 - A trihamiltonian extension of the Toda lattice

AU - Andrà, Chiara

AU - Degiovanni, Luca

AU - Magnano, Guido

N1 - Funding Information: The authors are indebted with the anonymous referee for suggesting the relation between the Lie bracket and Hermitian matrices, which allowed a remarkable simplification of the whole construction. The work for this paper was partially supported by the PRIN research project “Geometric methods in the theory of nonlinear waves and their applications” of the Italian MIUR.

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AB - A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H of n × n Hermitian matrices. The new Poisson structure is of Lie-Poisson type with respect to the standard Lie bracket of H. This Poisson structure (together with two already known ones, obtained through a r-matrix technique) allows to construct an extension of the periodic Toda lattice with n particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given.

KW - Classical integrable systems

KW - Classical r-matrix

KW - Periodic Toda lattice

KW - Symplectic geometry

KW - Trihamiltonian systems

UR - https://www.scopus.com/pages/publications/33750814104

U2 - 10.1016/j.geomphys.2006.06.008

DO - 10.1016/j.geomphys.2006.06.008

M3 - Article

SN - 0393-0440

VL - 57

SP - 863

EP - 880

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 3

ER -

A trihamiltonian extension of the Toda lattice

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Keywords

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