Geodesic
Optical Buffering and Mechanisms for Its Occurrence
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 1, pp. 14-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate a mathematical nonlinear-optics model that is a scalar parabolic equation on a circle with a small diffusion coefficient and a deviating spatial argument. We establish that the problem under consideration is characterized by the so-called buffering phenomenon, i.e.under an appropriate choice of the parameters, the coexistence of an arbitrary fixed number of time-periodic stable solutions of the problem can be obtained. We reveal the mechanisms for the occurrence of this phenomenon.
Keywords: boundary problem, buffering, traveling waves, Ginzburg–Landau equation.
Mots-clés : bifurcation, quasinormal form 
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A. Yu. Kolesov; N. Kh. Rozov. Optical Buffering and Mechanisms for Its Occurrence. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 1, pp. 14-28. http://geodesic.mathdoc.fr/item/TMF_2004_140_1_a1/

[1] S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, “Generatsiya struktur v opticheskikh sistemakh s dvumernoi obratnoi svyazyu: na puti k sozdaniyu nelineino-opticheskikh analogov neironnykh setei”, Novye fizicheskie printsipy opticheskoi obrabotki informatsii, eds. S. A. Akhmanov, M. A. Vorontsov, Nauka, M., 1990, 263–325

[2] A. V. Razgulin, ZhVM i MF, 33:1 (1993), 69–80 | MR | Zbl

[3] A. L. Skubachevskii, Diff. uravneniya, 34:10 (1998), 1394–1401 | MR | Zbl

[4] E. P. Belan, Dinamicheskie sistemy, 16 (2000), 160–167

[5] E. P. Belan, Dinamicheskie sistemy, 17 (2001), 179–184 | Zbl

[6] Yu. S. Kolesov, Matem. sb., 184:3 (1993), 121–136 | Zbl

[7] Yu. S. Kolesov, “Ustoichivost i bifurkatsiya beguschikh voln”, Nelineinye kolebaniya v zadachakh ekologii, ed. Yu. S. Kolesov, YaGU, Yaroslavl, 1985, 3–10 | MR

[8] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, Tr. MIAN, 222, 1998, 1–193 | MR

[9] A. Yu. Kolesov, N. Kh. Rozov, V. G. Sushko, Fund. i prikl. matem., 5:2 (1999), 437–473 ; А. Ю. Колесов, Е. Ф. Мищенко, Н. Х. Розов, УМН, 65:2 (2000), 95–120 ; А. Ю. Колесов, Н. Х. Розов, Тр. МИАН, 233, 2001, 153–207 | MR | Zbl | DOI | MR | MR | Zbl

[10] V. F. Kambulov, A. Yu. Kolesov, N. Kh. Rozov, ZhVM i MF, 38:8 (1998), 1287–1300 ; А. Ю. Колесов, Н. Х. Розов, Матем. сб., 191:8 (2000), 45–68 | MR | Zbl | DOI | MR | Zbl