Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation
arXiv:2105.10338 · doi:10.1140/epjp/s13360-021-01550-5
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.
20 pages, 5 figures, 5 tables, to appear in European Physical Journal Plus