Geodesic
Two-photon propagation of light and the~modified Liouville equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 2, pp. 297-304

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We show that the system of nonlinear equations of two-photon propagation of light with real amplitudes of the envelopes can be solved in general form by the classical Liouville method. This system, like other similar systems of Darboux-integrable equations, is related to the modified Liouville equation, and the found solution also provides general solutions of such modified equations. We conclude that the Liouville method provides an effective way to integrate a class of concrete system that admit Darboux integration.
Keywords: Darboux integration, generalized Liouville equation, two-photon propagation of light. 
@article{TMF_2020_204_2_a8,
     author = {A. M. Kamchatnov and M. V. Pavlov},
     title = {Two-photon propagation of light and the~modified {Liouville} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {297--304},
     publisher = {mathdoc},
     volume = {204},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_2_a8/}
}
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A. M. Kamchatnov; M. V. Pavlov. Two-photon propagation of light and the~modified Liouville equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 2, pp. 297-304. http://geodesic.mathdoc.fr/item/TMF_2020_204_2_a8/