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




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1 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : 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 one is constant. These structures called affine or modified Lie-Poisson structures are involved in the integrability of certain Euler equations that arise as models of shallow water waves.

Keywords : Bi-Hamiltonian formalism Diffeomorphisms group of the circle Lenard scheme Camassa-Holm equation





Author: Boris Kolev -

Source: https://hal.archives-ouvertes.fr/



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