Yu. Grigoryev

Address: 198904, St.-Petersburg, Petrodvorec, Ulyanovskaya str.,1, room 1

E-mail: yury.grigoryev@gmail.com

University: St.-Petersburg State University, Institute of science-research of Physics

Publications:

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

Abstract

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.

Keywords: integrable systems, separation of variables, velocity-dependent potentials

Citation: Grigoryev Y. A., Sozonov A. P., Tsiganov A. V., On an integrable system on the plane with velocity-dependent potential, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 3, pp. 355-367

DOI:10.20537/nd1603005

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

Grigoryev Y. A., Tsiganov A. V.

On the Abel equations and the Richelot integrals
2009, Vol. 5, No. 4, pp. 463-478

Abstract

The paper deals with superintegrable $N$-degree-of-freedom systems of Richelot type, for which $n\leqslant N$ equations of motion are the Abel equations on a hyperelliptic curve of genus $n−1$. The corresponding additional integrals of motion are second-order polynomials in momenta.

Keywords: superintegrable systems, separation of variables, Abel equations

Citation: Grigoryev Y. A., Tsiganov A. V., On the Abel equations and the Richelot integrals, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 4, pp. 463-478

DOI:10.20537/nd0904002

Grigoryev Y. A., Tsiganov A. V.

Computing of the separated variables for the Hamilton-Jacobi equation on a computer
2005, Vol. 1, No. 2, pp. 163-179

Abstract

We discuss an algorithm for calculating of the separated variables for the Hamilton-Jacobi equation for the wide class of the so-called L-systems on the Riemann manifolds of the constant curvature. We suggest a software implementation of this algorithm in the system of symbolic computations Maple and consider several examples.

Keywords: integrable systems, Hamilton-Jacobi equation, separation of variables

Citation: Grigoryev Y. A., Tsiganov A. V., Computing of the separated variables for the Hamilton-Jacobi equation on a computer, Rus. J. Nonlin. Dyn., 2005, Vol. 1, No. 2, pp. 163-179

DOI:10.20537/nd0502001

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