This article is cited in 4 papers

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

K. K. Izmailova^ab, A. P. Chupakhin<sup>ab

a</sup> M. A. Lavrent'ev Institute of Hydrodynamics
^b Novosibirsk State University

Abstract: 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, invariant solution, partial invariant solution, factor system.

MSC: 35Q55, 35C05, 58J70