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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0310028 (nlin)
[Submitted on 21 Oct 2003]

Title:Poisson Pencils, Integrability, and Separation of Variables

Authors:Gregorio Falqui (SISSA Trieste Italy)
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Abstract: In this paper we will 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 will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.
Comments: 31 pages, submitted for the Special Issue of Phil. Trans. Roy. Soc. on "Separation of Variables"
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Report number: SISSA 90/FM/2003
Cite as: arXiv:nlin/0310028 [nlin.SI]
  (or arXiv:nlin/0310028v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0310028

Submission history

From: Gregorio Falqui [view email]
[v1] Tue, 21 Oct 2003 11:42:36 UTC (26 KB)
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