Some exact solutions of the ideal MHD equations through symmetry reduction method

DOI10.1016/j.jmaa.2007.03.100zbMath1293.76107OpenAlexW1987573855MaRDI QIDQ2382710

P. Y. Picard

Publication date: 2 October 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.03.100

zbMATH Keywords

symmetryLie groupexact solutionsideal MHD equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

Related Items (4)

One class of MHD equations: Conservation laws and exact solutions ⋮ Electromagnetic fields simulating a rotating sphere and its exterior with implications to the modeling of the heliosphere ⋮ Group classification of the two‐dimensional magnetogasdynamics equations in Lagrangian coordinates ⋮ Closed-form solutions for a nonlinear partial differential equation arising in the study of a fourth grade fluid model

Uses Software

• PDESpecialSolutions
• PainleveTest
• PDERecursionOperator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation
• Symmetry analysis of differential equations with MATHEMATICA
• Vortices and invariant surfaces generated by symmetries for the 3D Navier-Stokes equations
• Group invariant solutions without transversality
• Symmetry groups and similarity solutions of MHD equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Group-invariant solutions and optimal systems for multidimensional hydrodynamics
• Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups
• On Conditionally Invariant Solutions of Magnetohydrodynamic Equations. Multiple Waves.
• Weak transversality and partially invariant solutions
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• The reducibility of partially invariant solutions of systems of partial differential equations
• A differential constraints approach to partial invariance
• Exact solutions to the ideal magneto-gas-dynamics equations through Lie group analysis and substitution principles
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

This page was built for publication: Some exact solutions of the ideal MHD equations through symmetry reduction method