Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation

Andronikos Paliathanasis

doi:10.1140/epjp/s13360-021-01550-5

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arXiv · 2105.10338

Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation

Andronikos Paliathanasis

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Abstract

We study the Lie point symmetries and the similarity transformations for the partial differential equations of the nonlinear one-dimensional magnetohydrodynamic system with the Hall term known as HMHD system. For this 1+1 system of partial differential equations we find that is invariant under the action of a seventh dimensional Lie algebra. Furthermore, the one-dimensional optimal system is derived while the Lie invariants are applied for the derivation of similarity transformations. We present different kinds of oscillating solutions.

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Andronikos Paliathanasis. 2021-05-14. Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation. https://doi.org/10.1140/epjp%2Fs13360-021-01550-5

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