Keywords: Landau–Lifshitz equation, Riemann problem, integral of motion.
@article{TMF_2018_197_1_a4,
author = {V. V. Kiselev and A. A. Raskovalov},
title = {Solitons in the~domain structure of the~ferromagnet},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {89--107},
year = {2018},
volume = {197},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a4/}
}
V. V. Kiselev; A. A. Raskovalov. Solitons in the domain structure of the ferromagnet. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 1, pp. 89-107. http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a4/
[1] E. K. Sklyanin, O polnoi integriruemosti uravneniya Landau–Lifshitsa, Preprint LOMI E-3-79, LOMI, 1979
[2] A. E. Borovik, V. N. Robuk, “Lineinye psevdopotentsialy i zakony sokhraneniya dlya uravneniya Landau–Lifshitsa, opisyvayuschego nelineinuyu dinamiku ferromagnetika”, TMF, 46:3 (1981), 371–381 | DOI | MR
[3] A. M. Kosevich, B. A. Ivanov, A. S. Kovalev, Nelineinye volny namagnichennosti. Dinamicheskie i topologicheskie solitony, Naukova dumka, Kiev, 1983
[4] A. E. Borovik, S. Klama, S. I. Kulinich, “Integration of the Landau–Lifshitz equation with preferred-axis anisotropy by the method of the inverse scattering problem”, Phys. D, 32:1 (1988), 107–134 | DOI | MR
[5] A. B. Borisov, V. V. Kiselev, Kvaziodnomernye magnitnye solitony, Fizmatlit, M., 2014
[6] R. F. Bikbaev, A. I. Bobenko, A. P. Its, Uravnenie Landau–Lifshitsa. Teoriya tochnykh reshenii II, Preprint DonFTI-84-7(82), Donetskii fiz.-tekhn. in-t AN USSR, Donetsk, 1984
[7] R. F. Bikbaev, A. I. Bobenko, A. P. Its, “O konechnozonnom integrirovanii uravneniya Landau–Lifshitsa”, Dokl. AN SSSR, 272:6 (1983), 1293–1298 | MR | Zbl
[8] Yu. F. Mitropolskii, N. N. Bogolyubov (ml.), A. K. Prikarpatskii, V. G. Samoilenko, Integriruemye dinamicheskie sistemy: spektralnye i differentsialno–geometricheskie aspekty, Naukova dumka, Kiev, 1987 | MR
[9] A. I. Bobenko, “Veschestvennye algebro-geometricheskie resheniya uravneniya Landau–Lifshitsa v teta-funktsiyakh Prima”, Funkts. analiz i ego pril., 19:1 (1985), 6–19 | DOI | MR | Zbl
[10] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967 | MR
[11] P. F. Byrd, M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, Springer, Berlin, 1971 | MR
[12] V. V. Kiselev, A. A. Raskovalov, “Nelineinaya dinamika kvaziodnomernoi spiralnoi struktury”, TMF, 173:2 (2012), 268–292 | DOI | DOI | MR
[13] V. V. Kiselev, A. A. Raskovalov, “Nelineinye kollektivnye vozbuzhdeniya v gelikoidalnykh magnitnykh strukturakh”, FMM, 113:12 (2012), 1180–1192 | DOI
[14] V. V. Kiselev, A. A. Raskovalov, “Solitons and nonlinear waves in the spiral magnetic structures”, Chaos, Solitons and Fractals, 84 (2016), 88–103 | DOI | MR
[15] A. V. Mikhailov, “The Landau–Lifschitz equation and the Riemann boundary problem on a torus”, Phys. Lett., 92:2 (1982), 51–55 | DOI | MR
[16] A. B. Borisov, V. V. Kiselev, “Mnogosolitonnye resheniya asimmetrichnykh kiralnykh $SU(2)$, $SL(2,R)$-teorii $(d=1)$”, TMF, 54:2 (1983), 246–257 | DOI | MR
[17] A. B. Borisov, “The hilbert problem for matrices and a new class of integrable equations”, Lett. Math. Phys., 7:3 (1983), 195–199 | DOI | MR
[18] A. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR
[19] V. V. Kiselev, A. A. Raskovalov, “Vzaimodeistvie brizera s volnoi namagnichennosti v ferromagnetike s anizotropiei tipa «legkaya os» ”, TMF, 163:1 (2010), 94–113 | DOI | DOI | Zbl
[20] V. V. Kiselev, A. A. Raskovalov, “Vynuzhdennoe dvizhenie uedinennykh domenov i domennykh granits v pole nelineinoi volny namagnichennosti”, FMM, 109:6 (2010), 625–638 | DOI
[21] V. V. Kiselev, A. A. Raskovalov, “Forced motion of breathers and domain boundaries against the background of nonlinear magnetization wave”, Chaos, Solitons and Fractals, 45:12 (2012), 1551–1565 | DOI
[22] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR
[23] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | DOI | MR | MR | Zbl