Bäcklund transformation and N-shock-wave solutions for a (3+1)-dimensional nonlinear evolution equation

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• 作者：Ya Sun ; Bo Tian ; Yu-Feng Wang ; Hui-Ling Zhen
• 关键词：(3+1) ; Dimensional nonlinear evolution equation ; Hirota method ; Shock ; wave solutions ; Bäcklund transformation
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：84
• 期：2
• 页码：851-861
• 全文大小：9,108 KB
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• 作者单位：Ya Sun (1)
  Bo Tian (1) (2)
  Yu-Feng Wang (1)
  Hui-Ling Zhen (1)
  
  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China
  2. State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In this paper, a (3+1)-dimensional nonlinear evolution equation is investigated, which can be used to describe reacting mixtures and shallow water waves. Through the Hirota method and symbolic computation, bilinear forms and Bäcklund transformation are derived, which are different from those in the existing literature. Moreover, N-shock-wave solutions are obtained. Based on those shock-wave solutions, propagation and collision of the shock waves are discussed via the asymptotic and graphic analysis on different planes: (1) oblique elastic collisions between/among the two/three shock waves will arise on the x–y and y–z planes, while parallel elastic collisions exist on the x–z plane; (2) shock waves maintain their original directions, amplitudes and velocities except for some small phase shifts after each collision; (3) the shock wave with higher amplitude travels faster and moves across the slower.