Abstract : the properties of solitary wave solution to multidimensional regulari zed long wave equations is discussed and one of its solitary wave solution is ob tained by direct integral method 文摘:本文讨论了高维正则长波方程的孤立波解的性态，同时运用直接积分法获得了它的一个孤立波解。
The results indicate that the amplitude of the initial solitary wave will decrease exponentially with respect to time t when s > 0 and will increase exponentially when s < 0 . some new soliton ( s ) will be generated in the latter case 结果表明当> 0时，初始孤立波的振幅随时间指数式衰减；当< 0时，初始孤立波的振幅随时间指数式增长，并有新的孤立子产生。
The basic principle of our algorithm is based on such observation that a majority of meaningful solitary wave solutions can be expressed as the polynomial forms in terms of " bell - shaped " function sech and " kink - shaped " function tanh which possessing localized property 算法的基本原理是基于这样一种观察，即非线性波方程绝大部分有物理意义的孤立波解都可以表示成具有局部性特征的“钟状函数” - sech和“扭状函数” - tanh的多项式。
The present paper intends to construct a systematic approach to search a type of particular exact solutions to nonlinear wave equations by utilizing the theory of mathematics mechanization proposed by famous mathematician wu wentsun . by the approach , two classes of important nonlinear coupled scalar field equations arising in the field of nonlinear physics are studied systematically and a batch of exact solutions containing steady and diverging solitary wave solutions and periodic ones are obtained , which are helpful in clarifying the movement of matter under the nonlinear interactiveties and play an important role in sicentifically explaining of the corresponding physical phenomenon 本文将我国著名数学家吴文俊的数学机械化思想应用于非线性物理领域，给出了构造非线性波方程组一类特殊精确解的一种统一算法，利用这种算法系统地研究了出现于非线性物理领域中的两类重要的非线性耦合标量场方程组，获得了这些方程组一批精确解(包括稳定和发散形式的孤立波解以及周期解) 。
In section 1 , some nonlinear wave equations of this part discussing are recommended ; in section 2 , the elementary tool of this part utilizing is mentioned , namely , the hyperbolic function method ; in section 3 , seme exact solitary wave solutions to these nonlinear wave equations are attained 本部分由三节组成，第一节介绍了所讨论的几类非线性波动方程；第二节介绍了本部分所使用的基本工具，即，双曲函数方法；第三节给出了这些非线性波动方程的若干精确孤立波解。
The mostly conclusion of this part is as follows , on the conditon of travelling wave , the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation , kaup - kupershmidt equation , the fifth order kdv equation , fisher - kolmogorov equation , on the help of the computer algebraic system ( maple ) , are explicitly established by making use of the hyperbolic function method . this part is maken up of three sections 本部分的主要结论如下，利用双曲函数展开法，在行波条件下，对sawada - kotera方程， kaup - kupershmidt方程，五阶kdv方程， fisher - kolmogorov方程，等几类非线性波动方程求解，将其孤立波表示为双曲函数的多项式，从而将非线性波方程的求解问题转化为非线性代数方程组的求解问题，并借助于计算机代数系统求解非线性代数方程组，最终获得了这些非线性波动方程的若干精确孤立波解。
