Liouville canonical form for compatible nonlocal Poisson brackets of hydrodynamic type, and integrable hierarchies

Abstract

We solve the problem of reducing to the simplest and convenient for our purposes, canonical form for an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature in order to get an effective construction of the integrable hierarchies related to all these compatible Poisson brackets.

14 pages

References in corpus (2)

• On the local systems Hamiltonian in the weakly nonlocal Poisson brackets
• Compatible Poisson brackets of hydrodynamic type

Cited by in corpus (2)

• Quasi-Frobenius algebras and their integrable N-parametric deformations generated by compatible (N x N)-metrics of constant Riemannian curvature
• Compatible nonlocal Poisson brackets of hydrodynamic type, and integrable hierarchies related to them