×

Adiabatic approximations for Landau-Lifshitz equations. (English. Russian original) Zbl 1234.35036

Proc. Steklov Inst. Math. 259, Suppl. 2, S124-S140 (2007); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 13, No. 2 (2007).
Summary: The asymptotics with respect to a small parameter for solutions of a system of Landau-Lifshitz equations with slowly varying coefficients and small dissipative terms is investigated. These equations are a mathematical model of a uniaxial ferromagnet in a time-dependent magnetic field. The asymptotics constructed make it possible to describe the magnetization reversal effect and to reveal the influence of the parameters of the external magnetic field and dissipation on the stability of this process.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (Nauka, Moscow, 1955; Gordon and Breach, New York, 1962).
[2] L. D. Landau and E. M. Lifshitz, Physik. Z. Sowjetunion 8(2), 153 (1935).
[3] Ya. A. Monosov, Nonlinear Ferromagnetic Resonance (Nauka, Moscow, 1971) [in Russian].
[4] S. Krupicka, Physics of Ferrites and Related Magnetic Oxides (Academia, Prague, 1973; Vieweg, Braunschweig 1973).
[5] A. V. Gurevich and G. A. Melkov, Magnetic Oscillations and Waves (Nauka, Moscow, 1994; CRC, New York, 1996).
[6] E. C. Stoner and E. P. Wohlfarth, Phil. Trans. Roy. Soc. A240, 599 (1948). · Zbl 0031.38003
[7] G. E. Kuzmak, Prikl. Mat. Mekh. 23(3), 519 (1951).
[8] V. D. Azhotkin and V. M. Babich, Prikl. Mat. Mekh. 49(3), 377 (1985).
[9] V. I. Arnol’d, Additional Chapters of the Theory of Ordinary Differential Equations (Nauka, Moscow, 1978); translated under the title Geometrical Methods in the Theory of Ordinary Differential Equations (Springer, New York, 1988).
[10] G. M. Zaslavskii and R. Z. Sagdeev, Introduction to Nonlinear Physics: From the Pendulum to Turbulence and Chaos (Nauka, Moscow, 1977) [in Russian]. · Zbl 0709.58003
[11] A. I. Neishtadt, Prikl. Mat. Mekh. 39(4), 621 (1975).
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.