THE LIE SYMMETRY ANALYSIS, OPTIMAL SYSTEM, EXACT SOLUTIONS AND CONSERVATION LAWS OF THE (2+1)-DIMENSIONAL VARIABLE COEFFICIENTS DISPERSIVE LONG WAVE EQUATIONS

Meng Jin; Jiajia Yang; Jinzhou Liu; Xiangpeng Xin

doi:10.11948/20230147

2023 Volume 13 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(6): 3535-3557

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Meng Jin, Jiajia Yang, Jinzhou Liu, Xiangpeng Xin. THE LIE SYMMETRY ANALYSIS, OPTIMAL SYSTEM, EXACT SOLUTIONS AND CONSERVATION LAWS OF THE (2+1)-DIMENSIONAL VARIABLE COEFFICIENTS DISPERSIVE LONG WAVE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3535-3557. doi: 10.11948/20230147

Citation:

Meng Jin, Jiajia Yang, Jinzhou Liu, Xiangpeng Xin. THE LIE SYMMETRY ANALYSIS, OPTIMAL SYSTEM, EXACT SOLUTIONS AND CONSERVATION LAWS OF THE (2+1)-DIMENSIONAL VARIABLE COEFFICIENTS DISPERSIVE LONG WAVE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3535-3557. doi: 10.11948/20230147

THE LIE SYMMETRY ANALYSIS, OPTIMAL SYSTEM, EXACT SOLUTIONS AND CONSERVATION LAWS OF THE (2+1)-DIMENSIONAL VARIABLE COEFFICIENTS DISPERSIVE LONG WAVE EQUATIONS

1.
School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Author Bio: Email: jinmeng_2022@163.com(M. Jin); Email: yjj706690541@163.com(J. Yang); Email: jinzhou_98@163.com(J. Liu)
Corresponding author: Email: xinxiangpeng@lcu.edu.cn(X. Xin)
Fund Project: The authors were supported by National Natural Science Foundation of China (11505090), Liaocheng University level science and technology research fund (318012018), Discipline with Strong Characteristics of Liaocheng University - Intelligent Science and Technology under Grant (319462208), Research Award Foundation for Outstanding Young Scientists of Shandong Province (BS2015SF009) and the doctoral foundation of Liaocheng University under Grant (318051413)

Abstract

Abstract

In this article, the (2+1)-dimensional variable coefficients dispersive long wave equations (vcDLWs) are studied by the Lie symmetry analysis method. The infinitesimal generators and geometric vector fields are given. Optimal system of the (2+1)-dimensional vcDLWs are analyzed by Olver's method. Based on the optimal system, the (2+1)-dimensional vcDLW equations are reduced to (1+1)-dimensional equations. A number of new exact solutions of vcDLW equations are derived. Some kink solutions and 2-soliton solutions are obtained by using $\left( {1/G'} \right)$-expansion method and $\left( {G'/G} \right)$-expansion method. Many different types of exact solutions can be obtained by changing the coefficient functions. By exploring the evolution of the solutions with function of the coefficients and time $t$, the dynamic behaviors of the solutions are analysed. At last, the conservation laws of the (2+1)-dimensional vcDLWs are derived based on the nonlinear self-adjointness.
- The (2+1)-dimensional vcDLWs /
- the Lie symmetry analysis /
- conservation laws /
- (1/G^′)-expansion method /
- (G^′/G)-expansion method
MSC: 35Q51, 35Q55

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References

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