Hydromagnetic shock waves in a dissipative Adlam–Allen model

In this work, we revisit the topic of existence of hydrodynamic shock waves in a cold weakly collisional plasma. For this purpose, we consider the well-established Adlam–Allen model with the addition of a dashpot term associated with the dissipation of the motion of the electrons relative to the ions. We establish the connection between this model and the Korteweg–de Vries Burgers equation via an asymptotic multiscale analysis. This fact suggests the possibility that this system may support shock wave solutions. Accordingly, by considering a corresponding dynamical system arising through a co-traveling frame reduction, we identify such orbits via a phase-plane analysis. We then leverage such initial conditions within systematic simulations of the original modified Adlam–Allen model, revealing a variety of supported robust wavefronts depending on the magnitude of the dissipation considered.