Ray theoretic analysis of spatial and temporal self-focusing in general weakly nonlinear media

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Abstract
A general method is presented for describing self-focusing phenomena in various media by means of a geometrical-optics approach. The general formalism applies to a wide class of media: inhomogeneous, anisotropic, dispersive, and time varying. In contradistinction to previous methods, which derive pertinent wave equations and analyze them by assuming intensity-dependent wave speeds, here the appropriate Hamilton equations are derived, from which self-focusing phenomena evolve directly. Simple examples illustrate the feasibility of the method to deal with spatial and temporal effects in various media.