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In this paper, the analytical solution of nonlinear wave equation, describing the propagation of non-diffracting wave beams in a medium with dielectric constant's nonlinear variation in paraxial approximation, is obtained. The obtained analytical solution gives good fit with the results of numerical integration.
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David L. Hovhannisyan, "Intensity distribution in nondiffracting beams propagating in a nonlinear medium," Proc. SPIE 5445, Microwave and Optical Technology 2003, (7 April 2004); https://doi.org/10.1117/12.558482