Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon ResonanceReport as inadecuate




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Thetransition regimes of solitons in four-photon resonant processes in the case oftwo-photon absorption of the fundamental radiation are numericallyinvestigated. The standard system of equations for the amplitudes ofprobability of finding the system in state with certain energy is used toderive the expression for the induced polarization in the nonlinear medium. Asfor the equations for the amplitudes of the optical pulses, the general case isconsidered in which both the amplitudes and phases are space-time dependent. Wefocus on the finite difference methods and the case of simultaneouslypropagating solitons at all frequencies of the interacting waves simultons.The obtained results indicate that upon certain threshold conditions allinteracting pulses become the solitons of Lorentzian shape. The numericalanalysis has also shown that the soliton amplitudes significantly depend on theratio between the nonlinear polarizability at the fundamental frequencyω0 and that of combinationof ω0 and the trigger-fieldfrequencyω12ω0+ ω1. In the second partof the paper, we apply the method of phase planes to show that at typicalvalues of parameters, the solitons are stable.

KEYWORDS

Solitons, Transition Regime, Stability

Cite this paper

Feshchenko, V. and Feshchenko, G. 2016 Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance. American Journal of Computational Mathematics, 6, 267-274. doi: 10.4236-ajcm.2016.63028.





Author: Vladimir Feshchenko1, Galina Feshchenko2

Source: http://www.scirp.org/



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