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

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 Painleve′ expansion of the（2＋1）-dimensional Burgers equation is localized after introducing multiple new variables to extend the ori...

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Bibliographic Details
Published in中国物理B：英文版 no. 1; pp. 132 - 138
Main Author 刘希忠 俞军 任博 杨建荣
Format Journal Article
LanguageEnglish
Published 2015
Subjects
Burgers方程
交互
剩余
局部对称
相互作用
非线性波
非线性激发
非线性物理
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Summary: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 Painleve′ 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 Ba¨cklund transformation（BT） is obtained. From this BT, novel interactive solutions among different nonlinear excitations are found.
Bibliography: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 Painleve′ 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 Ba¨cklund transformation（BT） is obtained. From this BT, novel interactive solutions among different nonlinear excitations are found.
11-5639/O4
Liu Xi-Zhong,Yu Jun,Ren Bo,Yang Jian-Rong（ 1. Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;2. Department of Physics and Electronics, Shangrao Normal University, Shangrao 334001, China）
residual symmetry; Ba¨cklund transformation; symmetry reduction solution; generalized tanh expansion method
ISSN:1674-1056
2058-3834