Finite symmetry transformation groups and some exact solutions to (2+1)-dimensional cubic nonlinear schrödinger equantion

Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.