Geodesic
Dynamical model of single-mode laser. I. Regime of stable stationary lasing
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 2, pp. 278-292 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that approximate qualitative results obtained earlier by elimination of rapidly relaxing variables are not correct. In the critical case, stationary solutions are only stable but not asymptotically stable, and therefore allowance for a small external random force can lead to instability. 
@article{TMF_1991_89_2_a11,
     author = {A. A. Bakasov},
     title = {Dynamical model of single-mode laser. {I.~Regime} of stable stationary lasing},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {278--292},
     year = {1991},
     volume = {89},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_2_a11/}
}
TY  - JOUR
AU  - A. A. Bakasov
TI  - Dynamical model of single-mode laser. I. Regime of stable stationary lasing
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 278
EP  - 292
VL  - 89
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_89_2_a11/
LA  - ru
ID  - TMF_1991_89_2_a11
ER  - 
%0 Journal Article
%A A. A. Bakasov
%T Dynamical model of single-mode laser. I. Regime of stable stationary lasing
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 278-292
%V 89
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1991_89_2_a11/
%G ru
%F TMF_1991_89_2_a11
A. A. Bakasov. Dynamical model of single-mode laser. I. Regime of stable stationary lasing. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 2, pp. 278-292. http://geodesic.mathdoc.fr/item/TMF_1991_89_2_a11/

[1] Bakasov A. A., Phys. Lett., 130:8–9 (1988), 461–466 | DOI | MR

[2] Andreev A. V., Emelyanov V. I., Ilinskii Yu. A., UFN, 131:4 (1980), 653–694 | DOI

[3] Arecchi F. T., Courtens E., Phys. Rev., A2:5 (1970), 1730–1737 | DOI

[4] Bonifacio R., Schwendimann P., Haake F., Phys. Rev., A4:1 (1971), 302–313 | DOI

[5] Haken H., Encyclopedia of physics, V. XXX/2c, Springer-Verlag, Berlin–Heidelberg–New York, 1970

[6] Haken H., Synergetics, Springer-Verlag, Berlin–Heidelberg–New York, 1978 | MR | Zbl

[7] Lyapunov A. M., Obschaya zadacha ob ustoichivosti dvizheniya, Gos. izd. tekhn.-teor. lit., M.–L., 1950 | MR

[8] Chetaev N. G., Ustoichivost dvizheniya, Gos. izd. tekhn.-teor. lit., M.–L., 1955 | MR

[9] Malkin I. G., Teoriya ustoichivosti dvizheniya, Nauka, M., 1966 | MR | Zbl

[10] Haken H., Ohno H., Opt. Comm., 16:1 (1976), 205–207 | DOI | MR

[11] Ohno H., Haken H., Phys. Lett., A59:4 (1976), 261–263 | DOI

[12] Lorenz E. N., J. Atmosph. Sci., 20:1 (1963), 130–163 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[13] Haken H., Z. Phys., 181:1 (1964), 96–124 | DOI | MR

[14] Arecchi F. T., Schultz-DuBois E. O.(eds.), Laser Handbook, V. I, North-Holland, Amsterdam, 1972

[15] Velarde M. G., Nonequilbrium Cooperative Phenomena in Physics and Related Fields, Plenum Press, New York–London, 1974

[16] Cvitanovic P. (ed.), University of Chaos, Adam Hilger Ltd., Bristol, 1984 | MR | Zbl

[17] Faddeev D. K., Sominskii I. S., Sbornik zadach po vysshei algebre, Nauka, M., 1968 | MR

[18] DeGiorgio V., Scully M. O., Phys. Rev., A2:4 (1970), 1170–1177 | DOI

[19] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

[20] Bakasov A. A., Phys. Lett., A146:3 (1990), 209–261 | DOI | MR

[21] Abraham N. B., Mandel P., Narducci L. M., “Dynamical Instabilities and Pulsations in Lasers”, Progress in Optics, 25, 1988, 1–190 | DOI

[22] Zeghlache H., Mandel P., J. Opt. Soc. Amer., 2:1 (1985), 18–22 | DOI

[23] Sparrow C., The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer-Verlag, New York–Heidelberg–Berlin, 1982 | MR | Zbl

[24] Roschin N. V., PMM, 42:5 (1978), 950–952 | MR

[25] Pade J., Rauh A., Tsarouhas G., Phys. Lett., A115:3 (1986), 93–96 | DOI | MR

[26] Bakasov A. A., Govorkov B. B., Jr., Stability theory of critical cases and the bifurcation points of the stationary solutions of the Lorenz model, Preprint I.C.T.P. IV/90/247, Trieste, 1990

[27] Fowler A. C., Gibbon J. D., McGuinness M. J., Physica, D4:2 (1982), 139–163 | MR | Zbl