Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations

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Kolev, Boris;
(2007)
  • Publisher: HAL CCSD
  • Related identifiers: doi: 10.1098/rsta.2007.2012
  • Subject: Diffeomorphisms group of the circle | [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] | MSC(2000): 35Q35, 35Q53, 37K10, 37K65 | Mathematical Physics | 35Q35, 35Q53, 37K10, 37K65 | Bi-Hamiltonian formalism | Lenard scheme | Camassa-Holm equation | [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]

23 pages; International audience; This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. We investigate the special case where one of the structures is the canonical Lie-Poisson structure and the second on... View more
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