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Electromagnetic shock waves and their structure in anisotropic magnets. (English. Russian original) Zbl 1040.78503
J. Appl. Math. Mech. 61, No. 1, 135-143 (1997); translation from Prikl. Mat. Mekh. 61, No. 1, 139-148 (1997).
Summary: The analogy between nonlinear electromagnetic waves in magnetizable media and nonlinear elastic waves in anisotropic media is justified and used. The analogy occurs when dispersion and dissipation are ignored. By using existing results one can therefore immediately formulate all that relates to investigating relations in Riemann waves and electromagnetic shock waves. To describe the structure of electromagnetic shock waves in magnetic materials the Landau-Lifshits equation is employed, which differs considerably from the relations used to describe the structure of shock waves in elastic media. A consequence of this is that the set of permissible shock waves (i.e. possessing a structure) acquires a complex structure and differs considerably from the analogous set for elastic shock waves. It is shown, in particular, that the set of permissible electromagnetic shock waves is not the same as the set of initially evolution discontinuities. The requirement that a structure should exist distinguishes, on certain parts of the shock adiabat, a set which is a dashed line with a very short dash length. In addition, there is a large number of individual points on the shock adiabat of the electromagnetic shock waves. Each point corresponds to a discontinuity with a separate velocity of motion, recalling the slow-combustion front in gas dynamics.

##### MSC:
 78A40 Waves and radiation in optics and electromagnetic theory
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##### References:
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