Full Symmetry Groups and Similar Reductions of a (2+1)-Dimensional Resonant Davey—Stewartson System

Abstract

Applying the classical Lie symmetry method to the (2+1)-dimensional resonant Davey—Stewartson system introduced by Tang [X.Y. Tang et al., Chaos, Solitons and Fractals 42 (2007) 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived.