摘要
提出了寻求孤子方程(组)的孤波解的一类新方法,其形式为有限对数的Laurent展式,其辅助方程为常系数的二阶常微分方程;结合齐次平衡法与微分方程的特征多项式,获得了KdV方程、混合KdV-MKdV方程及(2+1)维KP方程的精确孤波解,其中包含周期波解;利用本文提出的方法,可寻求其它孤子方程的精确解,因此该方法具有普遍应用性。
In this paper,we propose new method of finding new travlling wave solutions to the solitary equation,the formal solution is assumed as finite logarithm Laurent expansion,where the auxiliary equation is the second order ordinary differential equation with constant coefficient.By employing the homogeneous balance method and the characteristic polynomial of ordinary differential equation,we have obtained the exact travlling wave solutions to the KdV equation,the combined KdV-MKdV equation and（2＋1）dimensional KP equation,which contain the cyclic wave solutions.This method can be applied to other nonlinear evolution equations in soliton theory.Therefore this method has the universal utility.
出处
《潍坊学院学报》
2009年第6期61-67,共7页
Journal of Weifang University
基金
国家自然科学基金资助(10371023)
上海曙光跟踪课题08G01资助
关键词
齐次平衡法
KDV方程
行波解
homogeneous balance method
Kdv equation
travlling wave solution
