KdV和KdV-Burgers方程的直接解法  

A Direct Method for Solving the KdV Equation and KdV-Burgers Equation

作　　者：谢元喜[1] 

机构地区：[1]湖南理工学院物理系,湖南岳阳414000

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2007年第1期6-9,共4页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10472029)

摘　　要：利用文献中引入的变换,将非线性偏微分方程化为非线性常微分方程,再直接求解该常微分方程,从而简洁地求得了KdV方程和KdV-Burgers方程的若干显式精确解析解,包括孤波解、奇异行波解等.By using a transformation introduced formerly,a nonlinear partial differential equation was reduced to a nonlinear ordinary differential equation, and then solved directly. A series of explicit and exact analytical solutions to the KdV equation and KdV-Burgers equation, including solitary wave solutions and singular travelling wave solutions etc. ,were derived easily.

关 键 词：KDV方程 KDV-BURGERS方程 直接解法 行波解 孤波解 

分 类 号：O175.29[理学—数学]