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Bright transient objects in different wave bands have been discovered inrecent years. To explain these short (from ms to s), and very powerful eventsdifferent models, galactic and extragalactic, have been considered. One ofpopular model is based on the suggestion of transformation of the magnetizedplasma blob, presumably a MHD shock wave, moving with relativistic speed, intoelectromagnetic pulse after collision with some obstacle, or at entering inmedia with different properties. Such transformation cannot be described in theframe of classical MHD equations, which don't contain the displacement current,and don't include such transformation. Updating of the classic MHD equations byusing of full set of Maxwell equation with displacement current, made recentlyby several authors, gave a possibility to describe hydrodynamic phenomena,together with electromagnetic ones by the same set of equations. Here we applythese equations for study of propagation of different waves with account ofdisplacement current, and of transformation between different kind of waves inthe nonuniform media. We derive a dispersion equation describing a propagationof a weak linear wave in a uniform magnetized plasma, and consider in detailsthe cases with perpendicular and parallel motion to the magnetic field. Itcontains MHD, HD, Alfven and EM waves in the limiting cases, and some new typesof behaviour in a general situation. We consider a plasma with zero viscosityand heat conductivity, with a finite scalar electric conductivity. We haveshown, that transformation of MHD into EM wave may happen only in a highlymagnetized plasma, and have found the region of parameters, where no wavesexist, and only damping static perturbations may be present.

Wave propagation and transformation in the frame of magnetohydrodynamics with a vortex electric field