Alexander Vershilov

Address: 199034, 7-9, Universitetskaya nab.

University: Saint-Petersburg State University

Publications:

Vershilov A. V., Grigoryev Y. A., Tsiganov A. V.

On an integrable deformation of the Kowalevski top
2014, Vol. 10, No. 2, pp. 223-236

Abstract

We discuss an application of the Poisson brackets deformation theory to the construction of the integrable perturbations of the given integrable systems. The main examples are the known integrable perturbations of the Kowalevski top for which we get new bi-Hamiltonian structures in the framework of the deformation theory.

Keywords: Poisson geometry, Kowalevski top

Citation: Vershilov A. V., Grigoryev Y. A., Tsiganov A. V., On an integrable deformation of the Kowalevski top, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp. 223-236

DOI:10.20537/nd1402009

Vershilov A. V., Tsiganov A. V.

On the Darboux-Nijenhuis Variables on the Poisson Manifold $so^*(4)$
2007, Vol. 3, No. 2, pp. 141-155

Abstract

We classify quadratic Poisson structures on $so^*(4)$ and $e^*(3)$, which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed

Keywords: integrable system, bi-hamiltonian geometry, separation of variables

Citation: Vershilov A. V., Tsiganov A. V., On the Darboux-Nijenhuis Variables on the Poisson Manifold $so^*(4)$, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 2, pp. 141-155

DOI:10.20537/nd0702002

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