22 citations · 70 across the 13 of their papers we have counts for
14 papers
On compatible linear and quadratic Poisson brackets on
Andriy Panasyuk, Taras Skrypnyk
In the present paper, using two constant tensors and on satisfying certain linear-quadratic equation and a technique of Poisson bivectors and Schouten…
Rational interpolants and solutions of dispersionless Hirota system
Andriy Panasyuk
The aim of this paper is to construct a class of explicit nontrivial rational solutions of the dispersionless Hirota system of PDEs. All the solutions in this class are of homogene…
Webs, Nijenhuis operators, and heavenly PDEs
Andriy Panasyuk, Adam Szereszewski
In 1989 Mason and Newman proved that there is a 1-1-correspondence between self-dual metrics satisfying Einstein vacuum equation (in complex case or in neutral signature) and pairs…
On linear-quadratic Poisson pencils on trivial central extensions of semisimple Lie algebras
Andriy Panasyuk, Vsevolod Shevchishin
The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on trivial 1-dimensional central extensions of semisimple Lie algebras.…
Invariant Nijenhuis Tensors and Integrable Geodesic Flows
Konrad Lompert, Andriy Panasyuk
We study invariant Nijenhuis -tensors on a homogeneous space of a reductive Lie group from the point of view of integrability of a Hamiltonian system of differenti…
Kronecker webs, Nijenhuis operators, and nonlinear PDEs
Andriy Panasyuk
The aim of this paper is two-fold. First, a survey of the theory of Kronecker webs and their relations with bihamiltonian structures and PDEs is presented. Second, a partial soluti…