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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Poisson Pencils, Algebraic Integrability, and Separation of Variables
Gregorio Falquia, Marco Pedronib a 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
Аннотация:
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.
Ключевые слова:
Hamilton–Jacobi equations, bihamiltonian manifolds, separation of variables, generalized Toda lattices.
Поступила в редакцию: 11.05.2010 Принята в печать: 07.10.2010
Образец цитирования:
Gregorio Falqui, Marco Pedroni, “Poisson Pencils, Algebraic Integrability, and Separation of Variables”, Regul. Chaotic Dyn., 16:3-4 (2011), 223–244
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd437 https://www.mathnet.ru/rus/rcd/v16/i3/p223
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