LIE SYMMETRY ANALYSIS, CONSERVATION LAWS AND EXACT SOLUTIONS OF FOURTH-ORDER TIME FRACTIONAL BURGERS EQUATION

Chunyan Qin; Shoufu Tian; Li Zou; Tiantian Zhang

doi:10.11948/2018.1727

2018 Volume 8 Issue 6

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Chunyan Qin, Shoufu Tian, Li Zou, Tiantian Zhang. LIE SYMMETRY ANALYSIS, CONSERVATION LAWS AND EXACT SOLUTIONS OF FOURTH-ORDER TIME FRACTIONAL BURGERS EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1727-1746. doi: 10.11948/2018.1727

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Chunyan Qin, Shoufu Tian, Li Zou, Tiantian Zhang. LIE SYMMETRY ANALYSIS, CONSERVATION LAWS AND EXACT SOLUTIONS OF FOURTH-ORDER TIME FRACTIONAL BURGERS EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1727-1746. doi: 10.11948/2018.1727

LIE SYMMETRY ANALYSIS, CONSERVATION LAWS AND EXACT SOLUTIONS OF FOURTH-ORDER TIME FRACTIONAL BURGERS EQUATION

1 School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, China;
2 School of Mathematics and Statistics, Suzhou University, Anhui, Suzhou 234000, China;
3 School of Naval Architecture, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
4 Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

Fund Project:

Abstract

Abstract

In this paper, the fourth-order time fractional Burgers equation has been investigated, which can be used to describe gas dynamics and traffic flow. By employing the Lie group analysis method, the invariance properties of the equation are provided. With the aid of the sub-equation method, a new type of explicit solutions are well constructed with a detailed derivation. Furthermore, based on the power series theory, we investigate its approximate analytical solutions. Finally, its conservation laws with two kinds of independent variables are performed by making use of the nonlinear self-adjointness method.
- Lie group analysis method /
- invariance properties /
- sub-equation method /
- power series theory /
- conservation laws
MSC: 35Q51;35Q53;35C99

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References

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