Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

doi:10.1088/1674-1056/24/1/010203

›› 2015, Vol. 24 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/24/1/010203

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

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:2014-06-09 修回日期:2014-08-18 出版日期:2015-01-05 发布日期:2015-01-05
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).

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

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:2014-06-09 Revised:2014-08-18 Online:2015-01-05 Published:2015-01-05
Contact: Liu Xi-Zhong E-mail:liuxizhong123@163.com
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： In nonlinear physics, it is very difficult to study interactions among different types of nonlinear waves. In this paper, the nonlocal symmetry related to the truncated Painlevé expansion of the (2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system. Then the corresponding group invariant solutions are found, from which interaction solutions among different types of nonlinear waves can be found. Furthermore, the Burgers equation is also studied by using the generalized tanh expansion method and a new Bäcklund transformation (BT) is obtained. From this BT, novel interactive solutions among different nonlinear excitations are found.

关键词: residual symmetry, Bä, cklund transformation, symmetry reduction solution, generalized tanh expansion method

Abstract: In nonlinear physics, it is very difficult to study interactions among different types of nonlinear waves. In this paper, the nonlocal symmetry related to the truncated Painlevé expansion of the (2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system. Then the corresponding group invariant solutions are found, from which interaction solutions among different types of nonlinear waves can be found. Furthermore, the Burgers equation is also studied by using the generalized tanh expansion method and a new Bäcklund transformation (BT) is obtained. From this BT, novel interactive solutions among different nonlinear excitations are found.

Key words: residual symmetry, Bäcklund transformation, symmetry reduction solution, generalized tanh expansion method

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. Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation[J]. , 2015, 24(1): 10203-010203.

Liu Xi-Zhong (刘希忠), Yu Jun (俞军), Ren Bo (任博), Yang Jian-Rong (杨建荣). Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation[J]. Chin. Phys. B, 2015, 24(1): 10203-010203.

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Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

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