简洁地求一类非线性偏微分方程的特解

通过巧妙地引入一个变换,并将其中的试探函数表示为双曲正、余弦函数的形式,只需进行简单的求偏导数运算,就可将难于求解的非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,最后得到了一类非线性偏微分方程的某些特解,所得结果与已有结果完全吻合。不难看出,这种方法特别简洁。本方法可望进一步推广用于求解其它非线性偏微分方程。

Seeking Particular solutions to a Class of Nonlinear Partial Differential equations in a simple Fast Method

By introducing a transformation and utilizing hyperbolic function's good properties,the nonlinear partial differential equation that is hard to be solved by making use of the regular technique can be first reduced to a set of easily-solved algegraic equations,and then their related coefficients can be easily determined by using the approach of undetermined coefficients.Finally,the special solutions to a class of nonlinear partial equations are successfully presented.The results obtained in this paper are in a very good agreement with those given in some existing references.It is not difficult to see that this method used herein is very simple and concise.We firmly believe that this approach may be generalized to construct the solutions to other nonlinear partial differential equations.