Keywords: finite-gap integration, theta function.
@article{TMF_2014_178_2_a0,
author = {R. F. Bikbaev and A. I. Bobenko and A. R. Its},
title = {Landau{\textendash}Lifshitz equation, uniaxial anisotropy case: {Theory} of exact solutions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {163--219},
year = {2014},
volume = {178},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_2_a0/}
}
TY - JOUR AU - R. F. Bikbaev AU - A. I. Bobenko AU - A. R. Its TI - Landau–Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 163 EP - 219 VL - 178 IS - 2 UR - http://geodesic.mathdoc.fr/item/TMF_2014_178_2_a0/ LA - ru ID - TMF_2014_178_2_a0 ER -
R. F. Bikbaev; A. I. Bobenko; A. R. Its. Landau–Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 2, pp. 163-219. http://geodesic.mathdoc.fr/item/TMF_2014_178_2_a0/
[1] L. D. Landau, E. M. Livshits, “K teorii dispersii magnitnoi pronitsaemosti ferromagnitnykh tel”, Sobranie trudov L. D. Landau v 2-kh t., v. 1, Nauka, M., 1969, 128–143
[2] L. A. Takhtajan, Phys. Lett. A, 64:2 (1977), 235–237 | DOI | MR
[3] A. E. Borovik, Pisma v ZhETF, 28:10 (1978), 629–632
[4] E. K. Sklyanin, On complete integrability of the Landau–Lifshitz equation, Preprint E-3-79, LOMI, Leningrad, 1979
[5] A. B. Shabat, Funkts. analiz i ego pril., 9:3 (1975), 75–78 | DOI | MR | Zbl
[6] V. E. Zakharov, S. V. Manakov, Pisma v ZhETF, 18:7 (1973), 413–417
[7] I. A. Akhiezer, L. E. Borovik, ZhETF, 52:2 (1967), 508–513
[8] I. A. Akhiezer, L. E. Borovik, ZhETF, 52:5 (1967), 1332–1344
[9] A. M. Kosevich, FMM, 53:3 (1982), 420–446 | MR
[10] N. N. Bogolyubov (ml.), A. K. Prikarpatskii, “O konechnozonnykh resheniyakh uravneniya tipa Geizenberga”, Matematicheskie metody i fiziko-mekhanicheskie polya, Naukova dumka, Kiev, 1983, 7–13
[11] I. V. Cherednik, Izv. AN SSSR. Ser. matem., 47:2 (1983), 384–406 | DOI | MR | Zbl
[12] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, J. Phys. Soc. Japan, 52:2 (1983), 388–393 | DOI | MR | Zbl
[13] M. M. Bogdan, A. S. Kovalev, Pisma v ZhETF, 31:8 (1980), 453–457
[14] A. V. Mikhailov, Phys. Lett. A, 92:2 (1982), 51–55 | DOI | MR
[15] Yu. L. Rodin, Lett. Math. Phys., 7:1 (1983), 3–8 | DOI | MR | Zbl
[16] A. I. Bobenko, Zap. nauchn. semin. LOMI, 123 (1983), 58–66 | MR | Zbl
[17] A. B. Borisov, FMM, 55:2 (1983), 230–234
[18] R. F. Bikbaev, A. I. Bobenko, A. R. Its, Dokl. AN SSSR, 272:6 (1983), 1293–1298 | MR | Zbl
[19] A. I. Bobenko, Funkts. analiz i ego pril., 19:1 (1985), 6–19 | DOI | MR | Zbl
[20] M. Jimbo, T. Miwa, K. Ueno, Physica D, 2:2 (1981), 306–352 | DOI | MR | Zbl
[21] M. Jimbo, T. Miwa, Physica D, 2:3 (1981), 407–448 | DOI | MR | Zbl
[22] E. D. Belokolos, A. I. Bobenko, V. Z. Enol'skii, A. R. Its, V. B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer Series in Nonlinear Dynamics, Springer, Berlin, 1994 | Zbl
[23] A. Gurvits, R. Kurant, Teoriya funktsii, Nauka, M., 1968 | MR
[24] E. I. Zverovich, UMN, 26:1(157) (1971), 113–179 | DOI | MR | Zbl
[25] V. B. Matveev, Abelian functions and solitons, Preprint H 373, Univ. Wroclaw, Wroclaw, 1976
[26] B. A. Dubrovin, UMN, 36:2(218) (1981), 11–80 | DOI | MR | Zbl
[27] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR
[28] B. A. Dubrovin, S. I. Natanzon, Funkts. analiz i ego pril., 16:1 (1982), 27–43 | DOI | MR | Zbl
[29] A. I. Bobenko, Ch. Klein (eds.), Computational Approach to Riemann Surfaces, Lecture Notes in Mathematics, 2013, Springer, Berlin, 2011 | DOI | MR | Zbl
[30] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 3, Ellipticheskie i avtomorfnye funktsii, funktsii Lame i Mate, Nauka, M., 1967 | MR | Zbl
[31] E. D. Belokolos, V. Z. Enolskii, TMF, 53:2 (1982), 271–282 | DOI | MR | Zbl
[32] G. Forest, D.W. McLaughlin, J. Math. Phys., 23:7 (1932), 1248–1277 | DOI | MR
[33] E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Enolskii, UMN, 41:2(248) (1986), 3–42 | DOI | MR | Zbl
[34] J. Zagrodzinski, J. Phys. A., 15:10 (1982), 3109–3118 | DOI | MR | Zbl
[35] L. A. Takhtadzhyan, ZhETF, 66:2 (1974), 476–489
[36] J. D. Fay, Theta-Functions on Riemann Surfaces, Lecture Notes in Mathematics, 352, Springer, 1973 | DOI | MR | Zbl