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Investigation of electromagnetic shock-wave structure in anisotropic ferromagnets with easy axis. (English) Zbl 1074.78509
Summary: Shock waves and their structure are investigated in anisotropic ferromagnets with an easy axis of magnetization. For anisotropy of this type, shock (Hugoniot) adiabat, evolutionary conditions, and condition of nondecreasing entropy are obtained. The Landau-Lifshitz equation with dissipation term is used to describe the structure. The set of admissible discontinuities (i.e. those possessing the structure) does not coincide with the set of a priori evolutionary discontinuities. As shown in a set of figures that set of admissible discontinuities is a dashed line on a priori evolutionary intervals (with very short dashes and short intervals between them), and a set of isolated points on one of a priori nonevolutionary intervals of the shock adiabat. The distance between points is of the same order as the length of the dashes mentioned above and is determined by the ratio of dissipation and dispersion inside the structure of the shock wave. Each of these points on the shock adiabat corresponds to the discontinuity with a specified velocity, that from this point of view is similar to the deflagration front in gasdynamics. The investigation is numerically supported, and concrete examples of these points are found and the number of points is estimated. Similar results were obtained earlier by qualitative methods in the case of small angles between the field and the normal to the wave front [cf. the authors, J. Appl. Math. Mech. 61, No. 1, 135–143 (1997); translation from Prikl. Mat. Mekh. 61, No. 1, 139–148 (1997; Zbl 1040.78503)].

78A40 Waves and radiation in optics and electromagnetic theory
Full Text: DOI
[1] Bogatirev, U.K., Impulse devices with nonlinear distributed parameters, (1974), Sov. Radio Moscow
[2] Gaponov, A.V.; Ostrovskii, L.A.; Freidman, G.I., Electromagnetic shock waves, Radiophysics, 10, 9-10, 1376-1413, (1967)
[3] Gvozdovskaya, N.I.; Kulikovskii, A.G., About electromagnetic waves and their structure in anisotropic magnets, J. appl. math. mech., 61, 1, 135-143, (1997) · Zbl 1040.78503
[4] Kulikovsky, A.G.; Sveshnikova, E.I., Nonlinear waves in elastic media, (1995), CRC Press Boca Raton · Zbl 0865.73004
[5] Landau, L.D.; Lifshitz, E.M., Electrodynamics of continuous media, (1984), Pergamon Press Oxford · Zbl 0122.45002
[6] Gurevich, A.G.; Melkov, G.A., Magnetic oscillations and waves, (1994), Nauka Moscow
[7] Maugin, G.A., Continuum mechanics of electromagnetic solids, (1988), Elsevier Amsterdam · Zbl 0652.73002
[8] Kulikovskii, A.G., Strong discontinuities in continuum flows and their structure, (), 261-291
[9] Nakata, I., Nonlinear electromagnetic waves in a ferromagnet, J. phys. soc. Japan, 60, 1, 77-81, (1991)
[10] Ahiezer, A.I.; Bariahtar, V.G.; Peletminskii, S.V., Spin waves, (1967), Nauka Moscow
[11] Kosevich, A.M.; Ivanov, B.A.; Kovalev, A.S., Nonlinear magnetization waves. dynamical and topological solitons, (1983), Naukova Dumka Kiev · Zbl 1194.78001
[12] Kulikovskii, A.G., A possible effect of oscillations in the structure of a discontinuity on the set of admissible discontinuities, Sov. phys. dokl., 29, 4, 283-285, (1984)
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