Special conditional similarity reductions and exact solutions of the (2 + 1)-dimensional VCBKK system

In this paper, we present a method of special conditional similarity reductions for nonlinear partial differential equations. As an concrete example of its applications in physical problems, we apply this method to the (2 + 1)-dimensional Broer–Kaup–Kupershmidt system with variable coefficients (VCBKK), which has the extensive physics background, and obtain abundant exact solutions derived from some reduction equations.