Miura-reciprocal transformations and localizable Poisson pencils

Abstract

We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain a local representative and are in one-to-one correspondence with the equivalence classes of deformations of local semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura group.

27 pages

References in corpus (4)

• On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation
• Reciprocal transformations and local Hamiltonian structures of hydrodynamic type systems
• Projective geometry of homogeneous second order Hamiltonian operators
• Reciprocal transformations and flat metrics on Hurwitz spaces

Cited by in corpus (1)

• Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics