The residual symmetry and exact solutions of the Davey-Stewartson III equation

Through the truncated Painlevé expansion, the residual symmetry of the Davey-Stewartson III system is derived. This symmetry is localized to a properly prolonged system and the corresponding Bäcklund transformation is obtained. Based on the transformation, some exact solutions are generated. Furthermore, several types of interaction wave solutions are obtained by using the consistent tanh expansion method.