Bäcklund transformations for the Burgers equation via localization of residual symmetries

doi:10.1088/1674-1056/23/11/110203

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 Bä 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

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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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