×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kulikovsky, A.G; Sveshnikova, Ye.I, Nonlinear waves in elastic media, (1995), CRC Press Boca Raton, FL
[2] Bogatrev, Yu.K, Pulse devices with non-linear distributed parameters, (1974), Sovetskoye Radio Moscow
[3] Katayev, I.G, Electromagnetic shock waves, (1963), Sovetskoye Radio Moscow
[4] Gaponov, A.V; Ostrovskii, L.A; Freidman, G.I, Electromagnetic shock waves, Izv. vuzov. radiofizika, 10, 9-10, 1376-1413, (1967)
[5] Sveshnikova, Ye.I, Shock waves in a weakly anisotropic elastic incompressible material, Prikl. mat. mekh., 58, 3, 144-153, (1994)
[6] Gurevich, A.G; Melkov, G.A, Magnetic oscillations and waves, (1994), Nauka Moscow
[7] Maugen, G.A, Continuum mechanics of electromagnetic solids, (1988), North-Holland New York
[8] Landau, L.D; Lifshits, Ye.M, ()
[9] Sveshnikov, Ye.I, Quasi-transverse shock waves in an elastic medium with special types of the initial strains, Prikl. mat. mekh., 47, 4, 637-678, (1983)
[10] Kulikovskii, A.G; Sveshnikova, Ye.I, The structure of quasi-transverse elastic shock waves, Prikl. mat. mekh., 51, 6, 926-932, (1987)
[11] Chugainova, A.P, The attainment of a self-similar mode by non-linear waves in the problem of the action of a sudden change in load at the boundary of an elastic half-space, Izv. akad. nauk SSSR. MTT, 3, 187-189, (1990)
[12] Nakata, I, Nonlinear electromagnetic waves in a ferromagnet, J. phys. soc. Japan, 60, 1, 77-81, (1991)
[13] Kosevich, A.M; Ivanov, B.A; Kovalev, A.S, Non-linear magnetization waves. dynamic and topological solitons, (1983), Naukova Dumka Kiev
[14] Kulikovskii, A.G, A possible effect of oscillations in the structure of a discontinuity in a set of permissible discontinuities, Dokl. akad. nauk SSSR, 275, 6, 1349-1352, (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.