首次积分法与非线性色散-耗散方程的新精确解

摘要

主要介绍用于求解非线性发展方程的首次积分方法，通过首次积分方法获得一个用于描述由冷离子和热电子组成的等离子体弱非线性离子声波演化的非线性色散一耗散方程的一些新的精确解，例如指数函数解，三角函数解，奇异孤波解以及扭状孤立波解等，推广补充了已有的结果．%In this paper, by using the first-integral method, some new exact solutions to a nonlinear dispersive- dissipative equation, which describes weak nonlinear ion-acoustic waves in a plasma consisting of cold ions and warm electrons, are obtained, such as exponential function solutions, triangular function solutions, singular sol- itary wave solutions and kink solitary wave solutions and so on.