The qualitative analysis of the nonlinear equations using integral relations for solitons in photorefractive nonlinear crystals

摘要

A general model was built for spatial solitons in photorefractive crystals using the inverse problem in the scattering theory. The inverse problem in the scattering theory is defined knowing the spectral data that characterize the scattering. We present a formalism regarding the use of the inverse method in solving the nonlinear differential equations. Envelope singular analytical solutions (solitons) and asymptotically solutions of the wave equation for integral equation were obtained. The results are in good agreement with the results obtained in other papers.