7 citations · 7 across the 1 of their papers we have counts for
4 papers
Separation of variables on a non-hyperelliptic curve
V. G. Marikhin, V. V. Sokolov
In the paper we consider several dynamical systems that admit a separation of variables on the algebraic curve of genus 4. The main result of the paper is an explicit formula for t…
Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models
V. V. Sokolov, A. V. Tsiganov
A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the…
On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops
Vladimir V. Sokolov, Andrey V. Tsiganov
A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of…
Generalized Kowalevski top: new integrable cases on and
V. Sokolov
A three-parameter family of integrable quadratic Hamiltonians on and is presented. When one of the parameters vanishes, the Hamiltonian coincides with the Kowalevski…