Riemann theta solutions and their asymptotic property for a (3equation id-i-eq1"> equation-source format-t-e-x" xmlns:search="http://marklogic.com/appservices/search">\(+\) 1)-dimensional water wave equation

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• 作者：Yiren Chen ; Zhengrong Liu
• 关键词：(3+1) ; Dimensional equation ; Bell polynomials ; Hirota bilinear equation ; Riemann theta solution ; Asymptotic property
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：2
• 页码：1069-1080
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this paper, we consider the (3\(+\)1)-dimensional water wave equation \(u_{yzt}+u_{xxxyz}-6u_{x}u_{xyz}-6u_{xy}u_{xz}=0.\) Based on Bell polynomials, we obtain its Hirota bilinear equation which enable us to acquire Riemann theta solutions including arbitrary differentiable functions. Furthermore, we analyze the asymptotic property of these solutions and reveal the relationship between these solutions and the soliton solutions.