Bäcklund transformations for the Burgers equation via localization of residual symmetries

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

›› 2014, Vol. 23 ›› Issue (11): 110203-110203.doi: 10.1088/1674-1056/23/11/110203

Bäcklund transformations for the Burgers equation via localization of residual symmetries

刘希忠^a, 俞军^a, 任博^a, 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

收稿日期:2014-03-05 修回日期:2014-05-21 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
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).

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

Received:2014-03-05 Revised:2014-05-21 Online:2014-11-15 Published:2014-11-15
Contact: Yu Jun E-mail:junyu@usx.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Burgers equation, residual symmetry, Bä, cklund transformation

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.

Key words: Burgers equation, residual symmetry, Bä, cklund transformation

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 05.45.Yv (Solitons) 47.35.Fg (Solitary waves)

刘希忠, 俞军, 任博, 杨建荣. Bäcklund transformations for the Burgers equation via localization of residual symmetries[J]. , 2014, 23(11): 110203-110203.

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[J]. Chin. Phys. B, 2014, 23(11): 110203-110203.

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Bäcklund transformations for the Burgers equation via localization of residual symmetries

Bäcklund transformations for the Burgers equation via localization of residual symmetries

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