A theory for large-amplitude Alfvénic shocks across the external magnetic field in a collisional magnetoplasma is presented. For this purpose, we use the continuity and momentum equations for the electrons and ions, together with Ampère's and Faraday's laws, to derive the governing nonlinear equations for large-amplitude compressional Alfvénic waves. It is found that the latter can appear in the form of large-amplitude Alfvénic shocks that propagate with the super-Alfvénic speed.
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Shukla et al. (2011) studied this question.
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