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2013
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    Alexander Chupakhin

    15 Lavrentyev pr., Novosibirsk, Russia, 630090
    Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences

    Publications:

    Izmaylova K. K., Chupakhin A. P.
    Abstract
    We investigate the partial invariant solution of the system of the equations of the magneto hydrodynamics (MHD). This solution describes plane, steady motions of infinitely conducting gas in attendance of a magnetic field. The key-equation is the Bendikson equation type with degenerated singular point. We research topology of integral curves in a neighborhood of this singular point and infinity applying method of Frommer. There are two regimes of gas motions.
    Keywords: magneto hydrodynamics, partial invariant solution, distributed source in a cross-section magnetic field, Bendikson equation, method of Frommer
    Citation: Izmaylova K. K., Chupakhin A. P.,  Gas flow from the distributed source in a cross-section magnetic field., Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 4, pp.  443-465
    DOI:10.20537/nd0804005
    Ivanova A. V., Chupakhin A. P.
    Abstract
    We investigate exact shallow water on a rotating sphere. Thismodel is used in oceanology and physics of atmosphere for describing large-scalemotions of gas and fluid.We construct and study solution,which describe the damped ring source on the sphere. The motion takes place in a spherical belt. System of equations of shallow water on the sphere has solutions of two types: supercritical (supersonic) and subcritical (subsonic).
    Keywords: shallow water on a sphere, two types motion, differential equation
    Citation: Ivanova A. V., Chupakhin A. P.,  On damping source in model of the shallow water on rotating sphere, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 2, pp.  133-144
    DOI:10.20537/nd0802002
    Izmaylova K. K., Chupakhin A. P.
    Abstract
    Nonlinear Schrodinger equation (NSE) has many applications in mathematical physics (nonlinear optics, wave theory and so on). Gagnon and Winternitz have constructed symmetry algebra $L_{12}$ and optimal system of subalgebras for NSE (1989). It’s an extension of Galilei algebra $L_{11}$ admitted gas dynamics equations. Its three-dimensional symmetry subalgebras generate 27 different submodels. List of all solutions corresponding to these algebras has been received in this paper. Most of this solutions have not investigate previously.
    Keywords: Schrodinger equation, Lie algebra, invariant solution, partial invariant solution, factor system
    Citation: Izmaylova K. K., Chupakhin A. P.,  Group theoretical solutions of Schrodinger equation generated by three-dimensional symmetry algebras, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 3, pp.  349-362
    DOI:10.20537/nd0703005

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