Symbolic computation of exact solutions for nonlinear evolution equations

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• 作者：Lei Zhang (1) (2)
  Yezhi Lin (3)
  
  1. Department of mathematics ; North University of China ; Taiyuan ; 030051 ; People鈥檚 Republic of China
  2. Department of Computer Science and Technology ; East China Normal University ; Shanghai ; 200241 ; People鈥檚 Republic of China
  3. School of Information and Engineering ; Wenzhou Medical University ; Wenzhou ; 325035 ; People鈥檚 Republic of China
  
• 关键词：Symbolic computation ; Invariant subspace ; Exact solutions ; Evolution equations
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：79
• 期：2
• 页码：823-833
• 全文大小：354 KB
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• 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

Based on the invariant subspace method, a symbolic computation scheme and its corresponding MAPLE package are developed to construct exact solutions for nonlinear evolution equations. In the symbolic computation scheme, a crucial step is constructing the linear differential equations as invariant subspaces that systems of evolution equations admin and taking their solutions as subspaces to construct exact solutions. The MAPLE package is proved to provide an easy way for constructing exact solutions of evolution equations automatically by only inputting several necessary parameters. Three different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for wave equation. The results of the examples reveal that there are polynomial subspaces, trigonometric subspaces, exponential subspaces and other complex subspaces as invariant subspaces that evolutions equations admit. In addition, our MAPLE software package provides a helpful and easy-to-use tool in science and engineering to deal with a wide variety of (1+1) dimensional nonlinear evolution equations.