辅助方程法的来源

Source of the Auxiliary Equation Method

在"古为今用"原则下,通过研究大量的文献得出辅助方程法的主要来源是双曲正切函数展开法和Riccati方程法,并总结了Riccati方程法的构造性和机械化性两个特点.充分发挥这两个特点获得了Riccati方程的Backlund变换和解的非线性叠加公式,构造了非线性发展方程的无穷序列新精确解.这里包括双曲函数、三角函数和有理函数通过几种形式组合而成的无穷序列复合型精确解.

Following the principle of ＂make the past serve the present＂,a large number of documents were researched and a conclusion was abtained. The major source of the auxiliary equation method is the tanh-function expansion method and Riccati equation method. Two characteristics of constructivity and mechanization on the Riceati equation method were summarized. Make use of the two characteristics,Backlund transformation of the Riccati equation and nonlinear superposition formula of the solutions are introduced, and new infinite sequence exact solutions of nonlinear evolution equations are constructed. Including exact solutions of composite types composed by hyperbolic function,triangular function and rational function in different forms.