Solutions of Magnetohydrodynamics Equation through Symmetries

Solutions of Magnetohydrodynamics Equation through Symmetries

The magnetohydrodynamics (1 + 1) dimension equation, with a force and force-free term, is analysed with respect to its point symmetries. Interestingly, it reduces to an Abel’s Equation of the second kind and, under certain conditions, to equations specified in Gambier’s family. The symmetry analysis...

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Veröffentlicht in:Symmetry (Basel) 2023-10, Vol.15 (10), p.1908
Hauptverfasser: Sinuvasan, Rangasamy, Halder, Amlan K., Seshadri, Rajeswari, Paliathanasis, Andronikos, Leach, Peter G. L.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Fluid dynamics
fluid equations
invariant functions
Lie groups
lie symmetries
Magnetic fields
Magnetohydrodynamics
MHD equations
Ordinary differential equations
Partial differential equations
singularity analysis
Symmetry
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Beschreibung
Zusammenfassung:The magnetohydrodynamics (1 + 1) dimension equation, with a force and force-free term, is analysed with respect to its point symmetries. Interestingly, it reduces to an Abel’s Equation of the second kind and, under certain conditions, to equations specified in Gambier’s family. The symmetry analysis for the force-free term leads to Euler’s Equation and to a system of reduced second-order odes for which singularity analysis is performed to determine their integrability.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15101908