Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation
Institute of Systems Science, Durban University of Technology, PO Box 1334, 4000, Durban, Republic of South Africa
2 Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
Accepted: 8 May 2021
Published online: 15 May 2021
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 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021