Lie symmetries of a generalised non-linear Schrodinger equation. II. Exact solutions

For pt.I see ibid., vol.21, p.1493 (1988). The authors obtain group-invariant solutions of the non-linear equation i psi t + Delta psi =a 0 psi +a 1 psi mod psi mod 2 +a 2 psi mod psi mod 4 for which the symmetry group was previously shown to be the extended Galilei group for a 1 a 2 not=0 and the extended Galilei-similitude group for a 1 =0 or a 2 =0. They use the symmetry subgroups to reduce the equation to ordinary differential equations which are solved, whenever possible, with the help of a singularity analysis. Solutions are obtained in terms of elementary functions, Jacobi elliptic functions and Painleve transcendents.