Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 154-157
Cet article a éte moissonné depuis la source Math-Net.Ru
Possibility of integrating by the inverse scattering problem method is investigated for equations describing interaction of colliding quasimonochromatic wave packets in a medium with cubic nonlinearity. It is shown that all the integrable cases are restricted to the already known integrable case of the equations of “unsymmetrical chiral field” which corresponds to propagation of waves without the Kerr self-interaction.
@article{TMF_1989_81_1_a13,
author = {D. D. Tskhakaya (Jr.)},
title = {Integrability conditions for equations that describe the interaction of~colliding wave packets of~different polarizations in~nonlinear optics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {154--157},
year = {1989},
volume = {81},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a13/}
}
TY - JOUR AU - D. D. Tskhakaya (Jr.) TI - Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1989 SP - 154 EP - 157 VL - 81 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a13/ LA - ru ID - TMF_1989_81_1_a13 ER -
%0 Journal Article %A D. D. Tskhakaya (Jr.) %T Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics %J Teoretičeskaâ i matematičeskaâ fizika %D 1989 %P 154-157 %V 81 %N 1 %U http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a13/ %G ru %F TMF_1989_81_1_a13
D. D. Tskhakaya (Jr.). Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 154-157. http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a13/
[1] Zakharov V. E., Schulman E. I., Physica D, 1:2 (1980), 191–202 | DOI
[2] Zakharov V. E., Schulman E. I., Physica D, 4:2 (1982), 270–274 | DOI | Zbl
[3] Zakharov V. E., Shulman E. I., DAN SSSR, 283:6 (1985), 1325–1328 | MR
[4] Zakharov V. E., Schulman E. I., Physica D, 29:3 (1988), 283–321 | DOI | MR
[5] Shulman E. I., TMF, 76:1 (1988), 88–99 | MR
[6] Zakharov V. E., Mikhailov A. V., Pisma v ZhETF, 45:6 (1987), 279–282 | MR
[7] Cherednik I. V., TMF, 47:2 (1981), 225–229 | MR
[8] Veselov A. P., DAN SSSR, 270:6 (1983), 1298–1300 | MR | Zbl
[9] Veselova A. N., Vestn. MGU. Ser. Mat. mekh., 1985, no. 2, 64–67 | MR | Zbl