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

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

2006-09-30

arxiv.org/abs/math-ph/0610001v1

Philosophical Transactions. Series A, Mathematical, Physical and Engineering Sciences 365, 1858 (2007) pp. 2333-2357

Physics

Mathematical Physics

23 pages

Scientific paper

10.1098/rsta.2007.2012

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.

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