Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups

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.