中文摘要：

借助于符号计算软件Maple,通过代数方法——构造非线性偏微分方程（组）一般形式精确解的直接方法,并对其中关键的操作步骤进行改进,即引入一种新形式的变换,该变换形式比代数方法所引用的变换形式u=a0＋^n∑i=1aiФ^i（ai（i=0,…,n）是常数）更为广泛,进一步拓广代数方法的应用.用此改进的代数方法可求出许多非线性偏微分方程（组）新形式的精确解.把这种改进的代数方法应用于（1＋1）维色散长波方程,得到该方程的一系列新形式的精确解,这种解更具有一般性.

英文摘要：

With the aid of computer symbolic systems Maple and by using an algebraic method of construction, a series of general exact solutions were obtained to nonlinear differential equation or coupled equations. It improves the key sequence of operation, and a new form transformation was introduced and named. The transformation form is widely and directly used to transform when compared to the algebra n i method in which u=a0＋^n∑i=1aiФ^i（ai（i=0,…,n） are constants.） and is further developed the application of the algebra method. The new form＇s exact solutions of nonlinear differential equation or coupled equations are obtained through the improved algebra method. The improved algebra method is used to （ 1 ＋ 1 ）-dimensional dispersive long-wave equations, and a series of new form exact solution were obtained. The solutions present generality.