This article is cited in 4 papers

Poisson Pencils, Algebraic Integrability, and Separation of Variables

Gregorio Falqui^a, Marco Pedroni<sup>b

a</sup> Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Roberto Cozzi 53, I-20125, Milano, Italy
^b Dipartimento di Ingegneria dell’Informazione e Metodi Matematici, Università di Bergamo, Viale Marconi 5, I-24044 Dalmine (BG), Italy

Abstract: In this paper we review a recently introduced method for solving the Hamilton–Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the bihamiltonian structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.

Keywords: Hamilton–Jacobi equations, bihamiltonian manifolds, separation of variables, generalized Toda lattices.

MSC: 14H70, 37J35, 37K10, 70H20

Received: 11.05.2010
Accepted: 07.10.2010

Language: English

DOI: 10.1134/S156035471103004X

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