We address the problem of the separation of variables for the Hamilton–Jacobi equation
within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special …

We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary
signature. Further, we construct explicit transformation between orthogonal separating and …

In this paper we continue our analysis of the stationary flows of M component, coupled KdV
(cKdV) hierarchies and their modifications. We describe the general structure of the t 1 and t …

We give a representation–theoretic interpretation of recent discovered coupled soliton
equations using vertex operators construction of affinization of not simple but quadratic Lie …

We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some
recent results on the separation of variables for bihamiltonian manifold, we show that these …

In this article we study Stäckel representations of stationary KdV systems. Using Lax
formalism we prove that these systems have two different representations as separable …

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of
integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and …

We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym
hierarchies can be obtained by applying a reduction process to a simple Poisson pair …

We study the separability of the Neumann–Rosochatius system on the n-dimensional
sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables …

Starting from the tri-Hamiltonian formulation of the Lagrange top (LT) in a six-dimensional
phase space, we discuss the possible reductions of the Poisson tensors, the vector field and …