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    Yu. Grigoryev

    198904, St.-Petersburg, Petrodvorec, Ulyanovskaya str.,1, room 1
    St.-Petersburg State University, Institute of science-research of Physics


    Grigoryev Y. A., Sozonov A. P., Tsiganov A. V.
    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
    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
    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
    Grigoryev Y. A., Tsiganov A. V.
    On the Abel equations and the Richelot integrals
    2009, Vol. 5, No. 4, pp.  463-478
    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
    Grigoryev Y. A., Tsiganov A. V.
    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

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