Lie symmetry analysis, conservation laws and exact solutions of the generalized time fractional Burgers equation

Under investigation in this work are the invariance properties of the generalized time fractional Burgers equation, which can be used to describe the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Lie group analysis method is applie...

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Bibliographic Details
Published in:Europhysics letters 2016-04, Vol.114 (2), p.20003-20003
Main Authors: Wang, Xiu-Bin, Tian, Shou-Fu, Qin, Chun-Yan, Zhang, Tian-Tian
Format: Article
Language:English
Subjects:
02.30.Ik
05.45.Yv
52.35.Mw
Acoustic propagation
Acoustic waves
Burgers equation
Conservation
Conservation laws
Construction
Exact solutions
Fields (mathematics)
Lie groups
Mathematical analysis
Power series
Symmetry
Wave propagation
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Summary:Under investigation in this work are the invariance properties of the generalized time fractional Burgers equation, which can be used to describe the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Lie group analysis method is applied to consider its vector fields and symmetry reductions. Furthermore, based on the sub-equation method, a new type of explicit solutions for the equation is well constructed with a detailed analysis. By means of the power series theory, exact power series solutions of the equation are also constructed. Finally, by using the new conservation theorem, conservation laws of the equation are well constructed with a detailed derivation.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/114/20003