MODELLING AND ANALYSIS OF DYNAMIC SYSTEMS ON TIME-SPACE SCALES AND APPLICATION IN BURGERS EQUATION

Mingshuo Liu; Huanhe Dong; Yong Fang; Haoyu Dong

doi:10.11948/20220067

2022 Volume 12 Issue 6

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Mingshuo Liu, Huanhe Dong, Yong Fang, Haoyu Dong. MODELLING AND ANALYSIS OF DYNAMIC SYSTEMS ON TIME-SPACE SCALES AND APPLICATION IN BURGERS EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2555-2577. doi: 10.11948/20220067

Citation:

Mingshuo Liu, Huanhe Dong, Yong Fang, Haoyu Dong. MODELLING AND ANALYSIS OF DYNAMIC SYSTEMS ON TIME-SPACE SCALES AND APPLICATION IN BURGERS EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2555-2577. doi: 10.11948/20220067

MODELLING AND ANALYSIS OF DYNAMIC SYSTEMS ON TIME-SPACE SCALES AND APPLICATION IN BURGERS EQUATION

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2.
School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

Corresponding author: Email: donghaoyu2020@126.com(H. Dong)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12105161, 11975143) and Natural Science Foundation of Shandong Province (No. ZR2019QD018)

Abstract

Abstract

As effective tools that can be used to solve both continuous and discrete dynamic systems, symmetry analysis, conserved quantities and B$ \ddot{a} $cklund transformations of dynamic systems on time-space scales are studied, which unify and generalize the continuous and discrete cases. Applying the method to heat equation and Burgers equation, we get symmetries, group invariant solutions and B$ \ddot{a} $cklund transformations of the system on time-space scales. The results are applied to approximately simulate motion process of traffic flow with given initial condition. The study of nonlinear systems on time-space scales provides a theoretical basis for revealing the internal physical mechanism of the systems. Applications of the method to other dynamic equations on time-space scales deserve to be further studied.
- Burgers equation on time-space scales /
- symmetry analysis /
- conserved quantities /
- B$ \ddot{a} $cklund transformation
MSC: 76M60, 58J72, 34N05

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References

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