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变系数Yu-Toda-Sasa-Fukuyama方程的双线性形式与解析解

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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.
The Bilinear Equation and Analytical Solutions of the Variable-Coefficient Yu-Toda-Sasa-Fukuyama Equation
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.

variable-coefficient Yu-Toda-Sasa-Fukuyama equationHirota bilinear methodPainlevé propertyauto-Bäcklund transformationanalytical solution

宋禹欣、魏光美

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北京航空航天大学数学科学学院,北京 102200

变系数YTSF方程 Hirota双线性方法 Painlevé性质 自Bäcklund变换 解析解

2024

数学的实践与认识
中国科学院数学与系统科学研究院

数学的实践与认识

CSTPCD北大核心
影响因子:0.349
ISSN:1000-0984
年,卷(期):2024.54(10)