变系数Yu-Toda-Sasa-Fukuyama方程的双线性形式与解析解
The Bilinear Equation and Analytical Solutions of the Variable-Coefficient Yu-Toda-Sasa-Fukuyama Equation
宋禹欣 1魏光美1
作者信息
- 1. 北京航空航天大学数学科学学院,北京 102200
- 折叠
摘要
文章的研究对象是在流体动力学、等离子体物理等领域有较为广泛应用的Yu-Toda-Sasa-Fukuyama(YTSF)方程,主要分析该方程的解析性质并求其精确解.利用WTC法考察了变系数YTSF方程的Painlevé性质,求得该方程的Painlevé可积条件;利用Painlevé截断方法计算变系数YTSF方程的自Bäcklund变换,并基于此求得特殊孤子解和周期解;基于自Bäcklund变换求得变系数YTSF方程的双线性方程,并由此得到多孤子解.最后对所得的解进行图像绘制和物理性质分析.
Abstract
Yu-Toda-Sasa-Fukuyama(YTSF)equation is investigated in this paper,which has been widely used in fluid dynamics and plasma physics,etc.The main research contents are the analytic property and exact solutions of this equation.With WTC method,the Painlevé property is provided,and by the truncated Painlevé method,the auto-Bäcklund transformation is given.Then the bilinear form of the original equation is constructed with Hirota bilinear method,and the single soliton solution,double soliton solution and triple soliton solution are derived from the bilinear equation.In the end,for the special solutions of the equation,we set different parameters to draw the images of the solutions and analyze them.
关键词
变系数YTSF方程/Hirota双线性方法/Painlevé性质/自Bäcklund变换/解析解Key words
variable-coefficient Yu-Toda-Sasa-Fukuyama equation/Hirota bilinear method/Painlevé property/auto-Bäcklund transformation/analytical solution引用本文复制引用
出版年
2024
NETL
NSTL
万方数据