@article{TIMM_2003_9_1_a8,
author = {S. G. Glebov and O. M. Kiselev and V. A. Lazarev},
title = {Birth of solitons during passage through local resonance},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {64--70},
year = {2003},
volume = {9},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a8/}
}
TY - JOUR AU - S. G. Glebov AU - O. M. Kiselev AU - V. A. Lazarev TI - Birth of solitons during passage through local resonance JO - Trudy Instituta matematiki i mehaniki PY - 2003 SP - 64 EP - 70 VL - 9 IS - 1 UR - http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a8/ LA - ru ID - TIMM_2003_9_1_a8 ER -
S. G. Glebov; O. M. Kiselev; V. A. Lazarev. Birth of solitons during passage through local resonance. Trudy Instituta matematiki i mehaniki, Asymptotic expansions, approximation theory, topology, Tome 9 (2003) no. 1, pp. 64-70. http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a8/
[1] Kaup D. J., Newell A. S., Phys. Rev. V, 18 (1978), 5162 | MR
[2] Eilbeck J. C., Lomdahl P. S., Newell A. C., “Chaos in the Inhomogeneously Driven Sine-Gordon Equation”, Phys. Lett. A, 87:1 (1981), 1–4. | DOI | MR
[3] Akhmanov S. A., Khokhlov P. B., Problemy nelineinoi optiki, Nauka, M., 1964
[4] Kalyakin L. A., “Dlinnovolnovye asimptotiki. Integriruemye uravneniya kak asimptoticheskii predel nelineinykh sistem”, Uspekhi mat. nauk, 44:1(265) (1989), 5–34 | MR | Zbl
[5] Kaup D. J., “A perturbation expansion for the Zakharov–Shabat inverse scattering transform”, SIAM J. Appl. Math., 31 (1976), 121–133 | DOI | MR | Zbl
[6] Karpman V. I., Maslov E. I., “Teoriya vozmuschenii dlya solitonov”, Zhurn. eksperiment. i teoret. fiziki, 73 (1977), 537–559 | MR
[7] Kalyakin L. A., The first order corrections and justification of soliton perturbation, prepr. Inst. Math. Ural branch RAS, Inst. Math., Ufa, 1992, 13 pp.
[8] Barashenkov I. V., Smirnov Yu. S., Bifurcation to multisoliton complexes in the ac-driven, damped nonlinear Schrödinger equation, Research Rep. RR 3/97, Univ. Cape Town., 1997, 56 pp.
[9] Friedland L., Shagalov A. G., “Excitation of solitons by adiabatic multiresonant forcing”, Phys. Rev. Lett., 81:20 (1998), 4357–4360 | DOI
[10] Kevorkian J., “Passage through resonance for a one-dimensional oscillator with slowly varying frequency”, SIAM J. Appl. Math., 20 (1971), 364–373 | DOI | Zbl
[11] Kalyakin L. A., “Lokalnyi rezonans v slabonelineinoi zadache”, Mat. zametki, 44:5 (1988), 697–699 | MR | Zbl
[12] Glebov S. G., “Ob odnoi slabo nelineinoi zadache s lokalnymi rezonansami”, Differents. uravneniya, 31:8 (1995), 1402–1408 | MR | Zbl
[13] Zakharov V. E., “Ustoichivost periodicheskikh voln konechnoi amplitudy na poverkhnosti glubokoi zhidkosti”, Prikl. mekhanika i tekhn. fizika, 2 (1968), 86–94
[14] Talanov V. I., “O samofokusirovke malykh puchkov v nelineinykh sredakh”, Pisma v ZhETF, 2 (1965), 218–222
[15] Kelley P. L., “Self-focusing of optical beams”, Phys. Rev. Lett., 15 (1965), 1005–1008 | DOI
[16] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989, 336 pp. | MR