K. Izmaylova
Publications:
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Izmaylova K. K., Chupakhin A. P.
Gas flow from the distributed source in a cross-section magnetic field.
2008, Vol. 4, No. 4, pp. 443-465
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.
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Izmaylova K. K., Chupakhin A. P.
Group theoretical solutions of Schrodinger equation generated by three-dimensional symmetry algebras
2007, Vol. 3, No. 3, pp. 349-362
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.
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