The analytic solutions for the amplitude and phase of a cw cylindrically symmetric beam propagating in a self focusing Kerr medium obtained from the aberrationless paraxial approximation and the variational method are compared with the numerical results of the theory. For beam energies close to the critical focusing value, the variational method expression for the longitudinal phase is shown, except for an extremely small longitudinal distance of propagation, to give better qualitative and quantitative agreement with the numerical solutions. In particular, we confirm the variational method prediction that the regularized phase does not change sign.

© 1992 Optical Society of America

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