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There are a number of fields such as thermal science, optics, physics, and chemistry in which non-linear differential equations are widely used to describe complex phenomena. Accordingly, the research of non-linear evolution equations has attracted much attention world-widely [1-8]. Lie group theory is an effective and direct approach to constructing exact solutions of non-linear evolution equations [9, 10]. It has been widely considering that symmetry plays a very important role in various scientific fields, especially in the soliton theory. So far there are many powerful methods to find the symmetry of PDE, such as the classical Lie group method [11-18], the generalized symmetry method [18], the non-classical Lie group method [13], and the Clarkson and Kruskal [12] direct method. In fact, vector analysis is a completely new approach to symmetry [18]. The main target of this paper is to extend the vector analysis method to (2+1)-D case, and a novel modification for the generalized symmetry method is proposed. Burgers equation [19] describes the far field of wave propagation in non-linear physics. This paper considers its extension, the (2+1)-D Painleve integrable Burgers equations:

Symmetry analysis of a (2+1)-D system