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    K. Izmaylova

    15 Lavrentyev pr., 630090, Novosibirsk
    Lavrentyev Institute of Hydrodynamics SB RAS


    Izmaylova K. K., Chupakhin A. P.
    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
    Izmaylova K. K., Chupakhin A. P.
    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

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