一些非线性发展方程孤立波解的分析  

Analyses on the solitary wave solutions of some nonlinear evolution equations

作　　者：刘晓平[1,2] 刘春平[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]扬州职业大学高邮分院,江苏高邮225600

出　　处：《扬州大学学报（自然科学版）》2008年第4期21-24,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：江苏省自然科学基金资助项目(BK2006064)

摘　　要：通过对Burgers方程和KdV方程解的分析,给出一般非线性发展方程的双曲函数型孤立波解之间的一个重要关系,即tanhα形式的解和(sinh 2α±r2-1)/(cosh 2α+r)形式的解在方程中是成对出现的,进而得到KdV-Burgers方程的新精确解,最后说明文献得到的精确解并不是KdV方程和KdV-Burgers方程的新精确解.By analyzing the solutions of the Burgers equation and the KdV equation, an important relationship among the hyperbolic function solitary wave solutions of the general nonlinear evolution equation is given, that is, the solution in form of tanh a and （sinh 2α±√ r^2-1）/（cosh 2α＋r） appear in pairs. In this way, the new exact solutions of KdV-Burgers equation are obtained. Finally it explains that the exact solutions obtained in literature are not the new exact solutions of KdV equation and the KdV-Burgers equation.

关 键 词：双曲函数方法 非线性发展方程 孤立波解 

分 类 号：O175.3[理学—数学]