Affiliation:
1. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Abstract
We consider nonlinear optical systems describing the propagation of beams in Kerr-type nonlinear media, experiencing diffraction in transverse and longitudinal directions. The first model investigated, under nonparaxial approximation, is the complex nonlinear Helmholtz equation, recast into a coupled, real system of partial differential equations. We construct and apply its conserved vectors to determine exact solutions. This approach of a double reduction combines a point symmetry with a particular conservation law to enact a reduction and derive solutions. A second model is also studied, that is related to the Maxwell’s equations under paraxial approximation — a version of the nonlinear Schrödinger equation. We show that when the paraxial effect vanishes, a number of additional exact solutions and conservation laws are admitted.
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics,Electronic, Optical and Magnetic Materials
Cited by
5 articles.
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