求一类非线性偏微分方程精确解的简化试探函数法

利用试探函数法，将一个难于求解的非线性偏微分方程化为一个易于求解的代数方程，然后用待定系数法确定相应的常数，简洁地求得了一类非线性偏微分方程的精确解．将此方法应用到Burgers方程、KdV方程和KdV—Burgers方程，所得结果与已有结果完全吻合．本方法可望进一步推广用于求解其它非线性偏微分方程．

A simplified trial function method for seeking the exact solutions to a class of nonlinear pdes

By utilizing the trial function method, a class of nonlinear partial differential equations (PDEs for short) that are hard to be solved by the usual ways can be reduced to a set of algebraic equations, which can be easily solved, and their related coefficients can be easily determined by the undetermined coefficients method. Then, the exact analytical solutions to the class of nonlinear PDEs were successfully derived. Moreover, the method was applied to the Burgers equation, the KdV equation and the KdV-Burgers equation and the results were in very good agreement with those given in the reference. The method may be generalized to construct the solutions of other nonlinear PDEs.