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

作　　者：宋禹欣 魏光美 SONG Yu-xin;WEI Guang-mei(School of Mathmatical Science,Beihang University,Beijing 102200,China)

机构地区：[1]北京航空航天大学数学科学学院,北京102200

出　　处：《数学的实践与认识》2024年第10期167-177,共11页Mathematics in Practice and Theory

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Painleve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.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 Painleve property is provided,and by the truncated Painlevémethod,the auto-Backlund 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 

分 类 号：O175[理学—数学]