For the 1D shallow-water MHD system with a relaxed magnetic-divergence constraint, the admitted Lie symmetry algebras are classified into four cases, and an optimal system of subalgebras is used to build similarity solutions for the rotating, gravitating case.
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Lie Symmetries for the Shallow Water Magnetohydrodynamics Equations in a Rotating Reference Frame
For the 1D shallow-water MHD system with a relaxed magnetic-divergence constraint, the admitted Lie symmetry algebras are classified into four cases, and an optimal system of subalgebras is used to build similarity solutions for the rotating, gravitating case.