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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 2, Pages 297–304
DOI: https://doi.org/10.4213/tmf9887 (Mi tmf9887) 		 
Two-photon propagation of light and the modified Liouville equation

A. M. Kamchatnovab, M. V. Pavlovc

a Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Oblast, Russia
c Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf9887
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00157_а
The research of M. V. Pavlov was supported by the Russian Foundation for Basic Research (Grant No. 20-01-00157_а).
Received: 13.02.2020
Revised: 19.03.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 2, Pages 1093–1099
DOI: https://doi.org/10.1134/S0040577920080097
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik, 05.45.Yv, 42.65.Tg
MSC: 37K10
Language: Russian
Citation: A. M. Kamchatnov, M. V. Pavlov, “Two-photon propagation of light and the modified Liouville equation”, TMF, 204:2 (2020), 297–304; Theoret. and Math. Phys., 204:2 (2020), 1093–1099
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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