Abstract:

A number of algebraic methods used for constructing exact finite series solutions of nonlinear evolution equations are based on the homogeneous balance principle, such as the tanh function method, the Jacobi elliptic function method, the Painlevé truncated expansion method, the CRE method, etc. In each of these methods, the order of required solutions is determined by the homogeneous balance principle. In this paper, the homogeneous balance principle is further extended by considering additional balance possibilities. An n-order expansion method is proposed to determine possible new orders of required solutions. By applying the proposed method to several examples, we show that higher orders and new solutions can be obtained.

Key words: nonlinear evolution equation, homogeneous balance principle, n-order expansion method, finite series solution