New applications of the homogeneous balance principle

The homogeneous balance principle has been widely applied to the exploration of nonlinear transformation, exact solutions (especially solitary wave solution), dromion and similarity reduction to the nonlinear partial differential equations in mathematical physics. In this paper, we use the homogeneous balance principle to derive Bäcklund transformations for nonlinear partial differential equations that have more nonlinear terms and more highest-order partial derivative terms. With the aid of the Bäcklund transformations derived here, we could obtain exact solutions to the nonlinear partial differential equations. The Davey－Stewartson equation and the Nizhnik－Novikov－Veselov equation are considered as the examples.