The recursion operator method for generalized symmetries and B?cklund transformations of the Burgers-equations

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• 作者：Hanze Liu ; Jibin Li ; Lei Liu
• 关键词：Burgers-equation ; Recursion operator method ; Generalized symmetry ; B?cklund transformation ; Conservation law ; Exact solution ; 37L20 ; 35A22 ; 35C05
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：42
• 期：1-2
• 页码：159-170
• 全文大小：436KB
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• 作者单位：Hanze Liu (1) (2)
  Jibin Li (3) (4)
  Lei Liu (5)
  
  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong, 252059, China
  2. Department of Mathematics, Binzhou University, Binzhou, Shandong, 256603, China
  3. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China
  4. Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan, 650093, China
  5. The Center for Economic Research, Shandong University, Ji’nan, Shandong, 250100, China
  
• ISSN：1865-2085

文摘

In this paper, the generalized symmetries of the second-order Burgers-equation are obtained through the symmetry transformation method. The B?cklund transformations (BTs) of the two equations are constructed by the recursion operator method. Then, the infinite number of exact solutions to these equations are investigated in terms of the generalized symmetries and B?cklund transformations. Furthermore, the B?cklund transformations and conservation law of the general Burgers-equations are discussed.