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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (5): 595-606.doi: https://doi.org/10.1007/s10483-009-0506-6

• Articles • 上一篇    下一篇

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

特木尔朝鲁1 白玉山2   

  1. 1. Department of Mathematics, Shanghai Maritime University, Shanghai 200135, P. R. China;
    2. College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China
  • 收稿日期:2008-06-01 修回日期:2009-03-09 发布日期:2009-05-01

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

Chaolu Temuer1, BAI Yu-Shan2   

  1. 1. Department of Mathematics, Shanghai Maritime University, Shanghai 200135, P. R. China;
    2. College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China
  • Received:2008-06-01 Revised:2009-03-09 Published:2009-05-01

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摘要： In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations (PDEs) with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu’s method, in differential equations

Abstract: In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations (PDEs) with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu’s method, in differential equations

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