广义变系数Burgers方程的精确解

华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 27-33.

广义变系数Burgers方程的精确解

石玉仁^{1, 2}, 汪映海¹, 杨红娟², 吕克璞², 段文山²

1.兰州大学理论物理研究所, 兰州 730000; 2.西北师范大学物理与电子工程学院, 兰州 730070

收稿日期:2005-05-09 修回日期:2005-10-12 出版日期:2006-09-25 发布日期:2012-11-27

Exact Solutions of Generalized Burgers' Equation with Variable Coefficients

SHI Yu-ren^1,2, WANG Ying-hai¹, YANG Hong-juan², Lu Ke-pu², DUAN Wen-shan²

1.Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China 2.College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Received:2005-05-09 Revised:2005-10-12 Online:2006-09-25 Published:2012-11-27

摘要/Abstract

摘要： 对双曲函数法进行了扩展,利用它找到了广义变系数Burgers方程在一定条件下的若干精确解,
包括变速孤立波解和周期波解, 许多解为首次所得.实例表明在对变系数偏微分方程的求解中,
该法仍然是一种简便易行的方法.

关键词: 双曲函数法, 广义变系数Burgers方程, 精确解

Abstract: This paper found some exact solutions of Burgers' equation with variable coefficients by the hyperbola function method, including solitary wave solutions and periodic solutions. Some of the solutions were derived for the first time. The results showed that this approach is simple and efficient even for solving partial differential equations with variable coefficients.

Key words: hyperbola function method, generalized variable coefficient Burgers equation, exact solution ,

中图分类号:

O175.2

石玉仁, 汪映海, 杨红娟, 吕克璞, 段文山. 广义变系数Burgers方程的精确解[J]. 华东师范大学学报(自然科学版), 2006, 2006(5): 27-33.

SHI Yu-ren, WANG Ying-hai, YANG Hong-juan, Lu Ke-pu, DUAN Wen-shan. Exact Solutions of Generalized Burgers' Equation with Variable Coefficients[J]. Journal of East China Normal University(Natural Sc, 2006, 2006(5): 27-33.