https://doi.org/10.1140/epjp/s13360-021-01550-5
Regular Article
Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation
1
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
Received:
6
January
2021
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
