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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137119This 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.23 pagesMathematical Physics35Q35, 35Q53, 37K10, 37K65Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equationstext