Geodesic
Group theoretical solutions of Schr\"odinger equation generated by three-dimensional symmetry algebras
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 3, pp. 349-362.

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Nonlinear Schrödinger 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: Schrцdinger equation, Lie algebra, factor system.
Mots-clés : invariant solution, partial invariant solution 
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K. K. Izmailova; A. P. Chupakhin. Group theoretical solutions of Schr\"odinger equation generated by three-dimensional symmetry algebras. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 3, pp. 349-362. http://geodesic.mathdoc.fr/item/ND_2007_3_3_a4/