Geodesic
Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 259-272 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The method of the inverse scattering transform is used to solve a boundary-value problem on the half-plane for the twodimensional stationary Heisenberg magnet with nontrivial background corresponding to helicoidal magnetic structures. The boundary conditions are formulated in terms of scattering data, and this leads to the appearance of gaps in the continuous spectrum of the auxiliary linear problem. Trace identities are obtained. The asymptotic behavior of some of the simplest solutions of “soliton” type is discussed. 
@article{TMF_1992_90_2_a9,
     author = {E. Sh. Gutshabash and V. D. Lipovskii},
     title = {Boundary-value problem for two-dimensional stationary {Heisenberg} magnet with nontrivial {background.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {259--272},
     year = {1992},
     volume = {90},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/}
}
TY  - JOUR
AU  - E. Sh. Gutshabash
AU  - V. D. Lipovskii
TI  - Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 259
EP  - 272
VL  - 90
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/
LA  - ru
ID  - TMF_1992_90_2_a9
ER  - 
%0 Journal Article
%A E. Sh. Gutshabash
%A V. D. Lipovskii
%T Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 259-272
%V 90
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/
%G ru
%F TMF_1992_90_2_a9
E. Sh. Gutshabash; V. D. Lipovskii. Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 259-272. http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/

[1] Borisov A. B., Taluts G. G. i dr., Sovremennye problemy teorii magnetizma, Naukova dumka, Kiev, 1986, 103–111

[2] Movsesyants Yu. Ya., ZhETF, 91:2(8) (1986), 493–499

[3] Mikhailov A. V., Metod reduktsii v teorii integriruemykh uravnenii i ego primenenie v zadachakh magnetizma i nelineinoi optiki, Diss. dokt. fiz.-mat. nauk, ITF, Chernogolovka, 1987

[4] Borisov A. B., Nelineinye vozbuzhdeniya i dvumernye topologicheskie solitony v magnetikakh, Diss. dokt. fiz.-mat. nauk, In-t fiziki metallov, Sverdlovsk, 1986

[5] Alekseev G. A., Tr. MIAN, CLXXVI, 1987, 211–258 | MR | Zbl

[6] Monopoli: topologicheskie i variatsionnye metody, Sbornik statei, Mir, M., 1989

[7] Borisov A. B., Fhys. Lett. A, 143:1,2 (1990), 52–56 | DOI | MR

[8] Borisov A. B., Kiselëv V. V., Ionov S. N., Obratnaya zadacha rasseyaniya dlya integrirovaniya uravneniya ellipticheskii sin-Gordon na netrivialnom fone, deponirovano v VINITI, No 2015-V89, VINITI, M., 1989

[9] Jaworski M., Kaup D., Direct and inverse scattering problem assosiated with elliptic sinh-Gordon equation, Inst. for Nonlinear Studies Preprint, INS, Potsdam, 1989 | MR

[10] Lipovskii V. D., Nikulichev S. S., Vestn. LGU. Ser. Fizika i khimiya, 1989, no. 4, 61–65 | MR

[11] Gutshabash E. Sh., Lipovskii V. D., “Voprosy kvantovoi teorii polya i statisticheskoi fiziki”, Zap. nauchn. semin. LOMI, 180, 1990, 53–62 | MR

[12] Perelomov A. M., UFN, 134:4 (1981), 577–609 | DOI | MR

[13] Gürsey F., Tze H. C., Ann. Phys., 128 (1980), 29–130 | DOI | MR | Zbl

[14] Pohlmeyer K., Commun. Math. Phys., 46:3 (1976), 207–221 | DOI | MR | Zbl

[15] Lüsher M., Pohlmeyer K., Nucl. Phys. B, 137 (1978), 46–54 | DOI | MR

[16] Belavin A. A., Polyakov A. M., Pisma v ZhETF, 22:10 (1975), 506–510

[17] Mikhailov A. V., Yaremchuk A. I., Nucl. Phys. B, 202 (1982), 508–522 | DOI | MR

[18] Dzyaloshinskii I. E., ZhETF, 47:3(9) (1964), 992–1002

[19] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[20] Izyumov Yu. A., UFN, 144:3 (1984), 439–474 | DOI

[21] Izyumov Yu. A., Difraktsiya neitronov na dlinnoperiodicheskikh strukturakh, Energoatomizdat, M., 1987

[22] Borisov A. B., Izyumov Yu. A., DAN SSSR, 283:3 (1985), 859–861

[23] Manakov S. V., Metod obratnoi zadachi rasseyaniya v primenenii k nekotorym problemam fiziki voln v nelineinykh sredakh, Diss. kand. fiz.-mat. nauk, ITF, Chernogolovka, 1974

[24] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[25] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 | MR

[26] Its A. R., Metod izomonodromnykh deformatsii v teorii vpolne integriruemykh nelineinykh evolyutsionnykh sistem, Diss. dokt. fiz.-mat. nauk, LOMI, L., 1987

[27] Sukhanov V. V., TMF, 84:1 (1990), 23–37 | MR

[28] Gutshabash E. Sh., Vestn. LGU. Ser. Fizika i khimiya, 1990, no. 4, 84–86 | MR | Zbl

[29] Dodd R., Eilbek Dzh., Gibbon Dzh., Morris X., Solitony i nelineinye volnovye uravneniya, Mir, M., 1988 | MR