13 citations · 17 across the 2 of their papers we have counts for
6 papers
Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
Maciej Blaszak, Krzysztof Marciniak
We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of…
Non-Hamiltonian systems separable by Hamilton-Jacobi method
Krzysztof Marciniak, Maciej Blaszak
We show that with every separable calssical Stackel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter…
From Stäckel systems to integrable hierarchies of PDE's: Benenti class of separation relations
Maciej Blaszak, Krzysztof Marciniak
We propose a general scheme of constructing of soliton hierarchies from finite dimensional Stäckel systems and related separation relations. In particular, we concentrate on the si…
Geometric reduction of Hamiltonian systems
Krzysztof Marciniak, Maciej Blaszak
Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector Πon M we present a geometric method of reducing this operator on the foliation S a…
Dirac reduction of dual Poisson-presymplectic pairs
Maciej Blaszak, Krzysztof Marciniak
A new notion of a dual Poisson-presymplectic pair is introduced and its properties are examined. The procedure of Dirac reduction of Poisson operators onto submanifolds proposed by…
Separability preserving Dirac reductions of Poisson pencils on Riemannian manifolds
Maciej Blaszak, Krzysztof Marciniak
Dirac deformation of Poisson operators of arbitrary rank is considered. The question when Dirac reduction does not destroy linear Poisson pencils is studied. A class of separabilit…