Geodesic
Autoresonance excitation of a breather in weak ferromagnetics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1208-1220 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A mathematical model of the magnetodynamics of a weak ferromagnetic in an external magnetic field with variable frequency is studied. Conditions for the appearance of autoresonance are found under which the amplitude of the local magnetic inhomogeneities is considerably increased. Mathematically, the problem is to analyze the solutions to the sine-Gordon equation subject to a specific nonautonomous perturbation. For the perturbed equation, asymptotic solutions in the form of a breather with a slowly varying amplitude and a phase shift are constructed. The solutions whose amplitude increases with time from small values to quantities of order one are associated with the autoresonance phenomenon. 
@article{ZVMMF_2007_47_7_a7,
     author = {R. N. Garifullin and L. A. Kalyakin and M. A. Shamsutdinov},
     title = {Autoresonance excitation of a~breather in weak ferromagnetics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1208--1220},
     year = {2007},
     volume = {47},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a7/}
}
TY  - JOUR
AU  - R. N. Garifullin
AU  - L. A. Kalyakin
AU  - M. A. Shamsutdinov
TI  - Autoresonance excitation of a breather in weak ferromagnetics
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 1208
EP  - 1220
VL  - 47
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a7/
LA  - ru
ID  - ZVMMF_2007_47_7_a7
ER  - 
%0 Journal Article
%A R. N. Garifullin
%A L. A. Kalyakin
%A M. A. Shamsutdinov
%T Autoresonance excitation of a breather in weak ferromagnetics
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 1208-1220
%V 47
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a7/
%G ru
%F ZVMMF_2007_47_7_a7
R. N. Garifullin; L. A. Kalyakin; M. A. Shamsutdinov. Autoresonance excitation of a breather in weak ferromagnetics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1208-1220. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a7/

[1] Karpman V. I., Maslov E. M., Solovev V. V., “Dinamika bionov v dlinnykh dzhozefsonovskikh kontaktakh”, Zh. eksperim. i teor. fiz., 83:1 (1983), 289–300

[2] Kosevich A. M., Kivshar Yu. S., “Evolyutsiya soliton-antisolitonnoi pary pod deistviem vozmuschenii v sisteme, opisyvaemoi sinus-uravneniem Gordona”, Fiz. nizkikh t-r, 8:12 (1982), 1270–1284

[3] Nyuell A., “Obratnoe preobrazovanie rasseyaniya”, Solitony, Mir, M., 1983, 193–269 | MR

[4] Meerson B., Friedland L., “Strong autoresonance excitation of Rydberg atoms: the Rydberg accelerator”, Phys. Rev. A, 41 (1990), 5233–5236 | DOI

[5] Friedland L., “Subharmonic autoresonance”, Phys. Rev. E, 61:4 (2000), 3732–3735 | DOI | MR

[6] Fajans J., Friedland L., “Autoresonant (non stationary) excitation of a pendulum. Plutinos, plasmas and other nonlinear oscillators”, Amer. J. Phys., 69:10 (2001), 1096–1102 | DOI

[7] Kalyakin L. A., “Avtorezonans v dinamicheskoi sisteme”, Sovrem. matem. i ee prilozh., 5, M., 2003, 79–108

[8] Kalyakin L. A., “Justification of asymptotic expansions for the principal resonance equations”, Proc. Steklov Inst. Math., Suppl. 1, M., 2003, S108–S122 | MR | Zbl

[9] Garifullin P. H., “Postroenie asimptoticheskikh reshenii v zadache ob avtorezonanse”, Dokl. RAN, 398:3 (2004), 306–309 | MR

[10] Friedland L., Shagalov A. G., “Excitation of Multiphase waves nonlinear Schrödinger equation by capture into resonances”, Phys. Rev. E, 71 (2005), 036206, 12 pp. | DOI | MR

[11] Shamsutdinov M. A., Lomakina I. Yu., Nazarov V. N., “Dinamika lokalizovannykh magnitnykh neodnorodnostei v slabykh ferromagnetikakh v magnitnom pole pri nalichii zatukhaniya”, Fiz. metallov i metallovedenie, 100:5 (2005), 17–33

[12] Zvezdin A. K., “O dinamike domennykh granits v slabykh ferromagnetikakh”, Pisma v ZhETF, 29:10 (1979), 605–610

[13] Biryakhtar V. G., Ivanov B. A., Sukstanskii A. L., “Nelineinye volny i dinamika domennykh granits v slabykh ferromagnetikakh”, Zh. eksperim. i teor. fiz., 78:4 (1980), 1509–1522

[14] Veksler V. I., “O novom metode uskoreniya relyativistskikh chastits”, Dokl. AN SSSR, 43 (1944), 346–348

[15] Veksler V. I., “O novom metode uskoreniya chastits”, Dokl. AN SSSR, 44:9 (1944), 393–396

[16] McMillan E. M., “Resonance acceleration of charged particels”, Phys. Rev., 70 (1946), 800

[17] Golovanevskii K. S., “Giromagnitnyi avtorezonans s peremennoi chastotoi”, Fiz. plazmy, 11:3 (1985), 295–299

[18] Bogolyubov H. H., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[19] Zaslavskii G. M., Sagdeev R. Z., Vvedenie v nelineinuyu fiziku. Ot mayatnika do turbulentnosti i khaosa, Nauka, M., 1977 | MR

[20] Kalyakin L. A., “Usrednenie v modeli avtorezonansa”, Matem. zametki, 73:3 (2003), 449–452 | MR | Zbl

[21] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[22] Chirikov B. V., “Prokhozhdenie nelineinoi kolebatelnoi sistemy cherez rezonans”, Dokl. AN SSSR, 125:5 (1959), 1015–1018 | MR | Zbl

[23] Bryuno A. D., Stepennaya geometriya v algebraicheskikh i differentsialnykh uravneniyakh, Nauka, M., 1998 | MR | Zbl

[24] Kozlov V. V., Furta S. D., Asimptotiki reshenii silno nelineinykh sistem differentsialnykh uravnenii, Izd-vo MGU, M., 1996 | MR | Zbl