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We study the Lie point symmetries and the similarity transformations for thepartial differential equations of the nonlinear one-dimensionalmagnetohydrodynamic system with the Hall term known as HMHD system. For this1+1 system of partial differential equations we find that is invariant underthe action of a seventh dimensional Lie algebra. Furthermore, theone-dimensional optimal system is derived while the Lie invariants are appliedfor the derivation of similarity transformations. We present different kinds ofoscillating solutions.

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