Symmetry, full symmetry groups, and some exact solutions to a generalized Davey-Stewartson system

The Lie symmetry algebra of a generalized Davey-Stewartson (GDS) system is obtained. The general element of this algebra depends on eight arbitrary functions of time, which has a Kac-Moody-Virasoro loop algebra structure and is isomorphic to that of the standard integrable Davey-Stewartson equations under certain conditions imposed on parameters and arbitrary functions. Then based on the symmetry group direct method proposed by Lou and Ma [J. Phys. A 38, L129 (2005)] the full symmetry groups of the GDS system are obtained. From the full symmetry groups, both the Lie symmetry group and a group of discrete transformations can be obtained. Finally, some exact solutions involving sech-sech²-sech² and tanh-tanh²-tanh ² type solitary wave solutions are presented by a generalized subequation expansion method.