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Two-photon propagation of light and the modified Liouville equation
Theoretical and Mathematical Physics ( IF 1 ) Pub Date : 2020-08-01 , DOI: 10.1134/s0040577920080097
A. M. Kamchatnov , M. V. Pavlov

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.

中文翻译:

光的双光子传播和修正的刘维尔方程

我们表明,可以通过经典的 Liouville 方法以一般形式求解具有包络实际振幅的光的双光子传播非线性方程组。该系统与其他类似的 Darboux 可积方程系统一样,与修正的 Liouville 方程有关,并且找到的解也提供了此类修正方程的通解。我们得出结论,Liouville 方法提供了一种有效的方法来集成一类允许 Darboux 积分的具体系统。
更新日期:2020-08-01
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