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Chin. Phys. B, 2014, Vol. 23(11): 110203    DOI: 10.1088/1674-1056/23/11/110203
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Bäcklund transformations for the Burgers equation via localization of residual symmetries

Liu Xi-Zhong (刘希忠)a, Yu Jun (俞军)a, Ren Bo (任博)a, Yang Jian-Rong (杨建荣)b
a Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
b Department of Physics and Electronics, Shangrao Normal University, Shangrao 334001, China
Abstract  We obtain the non-local residual symmetry related to truncated Painlevé expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also localize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th Bäcklund transformation for Burgers equation can be expressed by determinants in a compact way.
Keywords:  Burgers equation      residual symmetry            cklund transformation  
Received:  05 March 2014      Revised:  21 May 2014      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
  47.35.Fg (Solitary waves)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11275129, 11305106, 11365017, and 11405110) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).
Corresponding Authors:  Yu Jun     E-mail:  junyu@usx.edu.cn

Cite this article: 

Liu Xi-Zhong (刘希忠), Yu Jun (俞军), Ren Bo (任博), Yang Jian-Rong (杨建荣) Bäcklund transformations for the Burgers equation via localization of residual symmetries 2014 Chin. Phys. B 23 110203

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