Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

doi:10.1088/1674-1056/acf9e8

中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120204-120204.doi: 10.1088/1674-1056/acf9e8

Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂)^†

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

收稿日期:2023-08-07 修回日期:2023-09-14 接受日期:2023-09-15 出版日期:2023-11-14 发布日期:2023-11-27
通讯作者: Zeng-Gui Wang E-mail:wangzenggui@lcu.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Shandong Province (Grant No.ZR2021MA084), the Natural Science Foundation of Liaocheng University (Grant No.318012025), and Discipline with Strong Characteristics of Liaocheng University—Intelligent Science and Technology (Grant No.319462208).

Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂)^†

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

Received:2023-08-07 Revised:2023-09-14 Accepted:2023-09-15 Online:2023-11-14 Published:2023-11-27
Contact: Zeng-Gui Wang E-mail:wangzenggui@lcu.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Shandong Province (Grant No.ZR2021MA084), the Natural Science Foundation of Liaocheng University (Grant No.318012025), and Discipline with Strong Characteristics of Liaocheng University—Intelligent Science and Technology (Grant No.319462208).

摘要/Abstract

摘要： The time-fractional modified Korteweg-de Vries (KdV) equation is committed to establish exact solutions by employing the bifurcation method. Firstly, the phase portraits and related qualitative analysis are comprehensively provided. Then, we give parametric expressions of different types of solutions matching with the corresponding orbits. Finally, solution profiles, 3D and density plots of some solutions are presented with proper parametric choices.

关键词: the time-fractional modified KdV equation, bifurcation analysis, exact solutions

Abstract: The time-fractional modified Korteweg-de Vries (KdV) equation is committed to establish exact solutions by employing the bifurcation method. Firstly, the phase portraits and related qualitative analysis are comprehensively provided. Then, we give parametric expressions of different types of solutions matching with the corresponding orbits. Finally, solution profiles, 3D and density plots of some solutions are presented with proper parametric choices.

Key words: the time-fractional modified KdV equation, bifurcation analysis, exact solutions

中图分类号: (Bifurcation theory)

02.30.Oz

02.30.Jr (Partial differential equations) 04.20.Jb (Exact solutions)

Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂). Exact solutions of a time-fractional modified KdV equation via bifurcation analysis[J]. 中国物理B, 2023, 32(12): 120204-120204.

Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂). Exact solutions of a time-fractional modified KdV equation via bifurcation analysis[J]. Chin. Phys. B, 2023, 32(12): 120204-120204.

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Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

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