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# Group theoretical solutions of Schrodinger equation generated by three-dimensional symmetry algebras

2007, Vol. 3, No. 3, pp.  349-362

Author(s): 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
DOI:10.20537/nd0703005