New wave behaviors and stability analysis for magnetohydrodynamic flows

Abstract

<p>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.</p>