Construction of asymptotic solutions of the autoresonance problem. Inner decomposition
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 33-48.

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The problem of autoresonance arising is investigated. Using the multi-scale method, we construct an asymptotic solution of this problem in the domain $t\ll\varepsilon^{-1}$.
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R. N. Garifullin. Construction of asymptotic solutions of the autoresonance problem. Inner decomposition. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 6, pp. 33-48. http://geodesic.mathdoc.fr/item/FPM_2006_12_6_a2/

[1] Andronov A. A., Gorelik G. A., “O rezonansnykh yavleniyakh pri dvizhenii relyativistskoi chastitsy v tsiklotrone”, DAN SSSR, 49 (1945), 664–666

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

[3] Veksler V. I., “O novom metode uskoreniya relyativistskikh chastits”, DAN SSSR, 43 (1944), 346–348; 393–396

[4] Garifullin R. N., “Issledovanie rosta reshenii nelineinogo uravneniya v zavisimosti ot nachalnykh dannykh”, Trudy III Regionalnoi shkoly-konf. po matematike i fizike dlya studentov, aspirantov i molodykh uchenykh, I. Matematika, 2003, 189–195

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

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

[7] Kalyakin L. A., “Asimptoticheskii analiz modeli avtorezonansa”, Dokl. RAN., 378:5 (2001), 594–597 | MR | Zbl

[8] Kuzmak G. E., “Asimptoticheskie resheniya nelineinykh differentsialnykh uravnenii s peremennymi koeffitsientami”, PMM, 23:3 (1951), 519–506

[9] Aranson I., Meersoh B., Tajima T., “Excitation of solitons by an external resonant wave with a slowly varying phase velocity”, Phys. Rev. A, 74 (1992), 7000–7510

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

[11] Friedland L., “Autoresonant excitation and evolution of nonlinear waves: The variational approach”, Phys. Rev. E, 55 (1997), 1929–1939 | DOI

[12] Kalyakin L. A., “Asymptotic analysis of an autoresonance model”, Russ. J. Math. Phys., 9:1 (2002), 84–95 | MR | Zbl

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

[14] MacMillan E. M., “The synchrotron: A proposed high energy particle accelerator”, Phys. Rev., 68 (1945), 143–144 | DOI