New wave behaviors and stability analysis for magnetohydrodynamic flows

Shengfang Yang; Huanhe Dong; Mingshuo Liu; Shengfang Yang; Huanhe Dong; Mingshuo Liu

doi:10.3934/nhm.2024040

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 887-922. doi: 10.3934/nhm.2024040

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New wave behaviors and stability analysis for magnetohydrodynamic flows

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 30 July 2024 Revised: 21 August 2024 Accepted: 29 August 2024 Published: 04 September 2024

The Lie symmetry analysis and generalized Riccati equation expansion methods were performed on the inviscid and viscous incompressible magnetohydrodynamic equations. Using the Lie symmetry analysis method, symmetries and similarity reductions of (2 + 1)- and (3 + 1)-dimensional magnetohydrodynamic equations were derived. Different forms of trigonometric function solutions and rational solutions were obtained, which yielded periodic solutions, single soliton solutions, and lump solutions. Furthermore, using the generalized Riccati equation expansion method, we obtained abundant new solutions of magnetohydrodynamic equations, including kink, kink-like, breather, and interaction solutions. Moreover, the stability of magnetohydrodynamic equations was investigated from both qualitative and quantitative perspectives. The exact solutions and stability analysis could provide accurate mathematical descriptions and theoretical basis for numerical analysis and regulation of magnetohydrodynamic systems.
- magnetohydrodynamic equations,
- Lie symmetry analysis method,
- breather solution,
- lump solution,
- kink and kink-like solutions,
- stability analysis
Citation: Shengfang Yang, Huanhe Dong, Mingshuo Liu. New wave behaviors and stability analysis for magnetohydrodynamic flows[J]. Networks and Heterogeneous Media, 2024, 19(2): 887-922. doi: 10.3934/nhm.2024040

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Abstract

The Lie symmetry analysis and generalized Riccati equation expansion methods were performed on the inviscid and viscous incompressible magnetohydrodynamic equations. Using the Lie symmetry analysis method, symmetries and similarity reductions of (2 + 1)- and (3 + 1)-dimensional magnetohydrodynamic equations were derived. Different forms of trigonometric function solutions and rational solutions were obtained, which yielded periodic solutions, single soliton solutions, and lump solutions. Furthermore, using the generalized Riccati equation expansion method, we obtained abundant new solutions of magnetohydrodynamic equations, including kink, kink-like, breather, and interaction solutions. Moreover, the stability of magnetohydrodynamic equations was investigated from both qualitative and quantitative perspectives. The exact solutions and stability analysis could provide accurate mathematical descriptions and theoretical basis for numerical analysis and regulation of magnetohydrodynamic systems.

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