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

The symmetry group of the generalised non-linear Schrodinger equation i psi t + Delta psi =a 0 psi +a 1 mod psi mod 2 psi +a 2 mod psi mod 4 psi in three space dimensions is shown to be the extended Galilei group G(3), for a 1 a 2 not=0, and the Galilei-similitude group G d (3) (including a dilation) for a 1 =oor a 2 =0. All Lie subgroups of G(3) and G d (3) are found. They will be used in a subsequent paper to obtain group invariant solutions of the equation.