Geodesic
Maxwell–Bloch equation and the inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 11-31 
I. R. Gabitov; V. E. Zakharov; A. V. Mikhailov. Maxwell–Bloch equation and the inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 11-31. http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a1/
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     title = {Maxwell{\textendash}Bloch equation and the inverse scattering method},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The inverse scattering method is used to construct general solutions of the Maxwell–Bloch system, these solutions being determined by specification of the polarization as $t\to\infty$. The solutions are classified. An approximate solution is obtained for the mixed boundary-value problem for the Maxwell–Bloch system describing the phenomenon of superfluorescence (generation of a pulse from initial fluctuations of the polarization in a mirrorless laser).

[1] Lamb G. L., Jr., Phys. Lett., 25A (1967), 181 | DOI

[2] Lamb G. L., Jr., Rev. Mod. Phys., 43 (1971), 99 | DOI | MR

[3] Ablowits M. J., Kaup D. J., Newell A. C., J. Math. Phys., 15 (1974), 1852 | DOI

[4] Manakov S. V., ZhETF, 83 (1982), 68

[5] Zakharov V. E., Pisma v ZhETF, 32 (1980), 603

[6] Gabitov I. R., Zakharov V. E., Mikhailov A. V., Pisma v ZhETF, 37:5 (1983), 234–237

[7] Gabitov I. R., Zakharov V. E., Mikhailov A. V., ZhETF, 86:4 (1984), 1204–1216

[8] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov (metod obratnoi zadachi), Nauka, M., 1980 | MR

[9] Basov N. G., Ambartsumyan R. V., Zuev V. S., Kryukov P. G., Letokhov V. S., ZhETF, 56 (1969), 403

[10] Zakharov V. E., Shabat A. B., ZhETF, 61:1 (1971), 118–134 | MR

[11] Haake F., Haus J. W., King H., Schröder Gr., Glauber R., Phys. Rev., A23 (1981), 1322 | DOI | MR

[12] Polder D., Schuurmans M. F. H., Vrehen Q. H. F., Phys. Rev., A19 (1979), 1192 | DOI

[13] Allen L., Eberli Dzh., Opticheskii rezonans i dvukhurovnevye atomy, Mir, M., 1973

[14] Vrehen Q. H. F., Gibbs H. M., Superfluorescence experiments, Preprint PRL, Eindoven, Netherlands, 1982

[15] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Gostekhizdat, M.–L., 1950 | MR

[16] Uitteker E. T., Vatson D. N., Kurs sovremennogo analiza, ch. 2, Fizmatgiz, M., 1963

[17] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR