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

Risultato della ricerca: Contributo su rivista › Articolo in rivista › 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.

Lingua originale	Inglese
pagine (da-a)	863-880
Numero di pagine	18
Rivista	Journal of Geometry and Physics
Volume	57
Numero di pubblicazione	3
DOI	https://doi.org/10.1016/j.geomphys.2006.06.008
Stato di pubblicazione	Pubblicato - feb 2007
Pubblicato esternamente	Sì

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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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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

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JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

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A trihamiltonian extension of the Toda lattice

Abstract

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