Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups
- 7 April 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (7) , 1493-1511
- https://doi.org/10.1088/0305-4470/21/7/013
Abstract
The symmetry group of the generalised non-linear Schrodinger equation i psi t+ Delta psi =a0 psi +a1 mod psi mod 2 psi +a2 mod psi mod 4 psi in three space dimensions is shown to be the extended Galilei group G(3), for a1a2 not=0, and the Galilei-similitude group Gd(3) (including a dilation) for a1=oor a2=0. All Lie subgroups of G(3) and Gd(3) are found. They will be used in a subsequent paper to obtain group invariant solutions of the equation.Keywords
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