Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia
Saint-Petersburg State University
Grigoryev Y. A., Sozonov A. P., Tsiganov A. V.
On an integrable system on the plane with velocity-dependent potential
2016, Vol. 12, No. 3, pp. 355-367
We discuss an algorithmic construction of the auto Bäcklund transformations of Hamilton–Jacobi equations and possible applications of this algorithm to finding new integrable systems with integrals of motion of higher order in momenta. We explicitly present Bäcklund transformations for two Hamiltonian systems on the plane separable in parabolic and elliptic coordinates.
Khudobakhshov V. A., Sozonov A. P.
Separation of variables for some generalisation of the Kowalevski top
2013, Vol. 9, No. 2, pp. 247-255
One integrable deformation of the Kowalevski top is studied in framework of the bi-hamiltonian geometry. The main result is the calculation of the variables of separation and of the corresponding quadratures in differential and integral forms.