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Renormalization group analysis for singularities in the wave beam self-focusing problem

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Abstract

A singular solution of the boundary value problem for the system of equations describing wave beam self-focusing is investigated by constructing renormalization group symmetries. New analytic expressions are found that characterize the spatial evolution of a beam with an arbitrary initial profile in a medium with cubic nonlinearity. The behavior of a Gaussian beam is thoroughly analyzed up to the moment the solution singularity is formed, and a hypothesis is proposed for describing the solution structure after the singularity occurs.

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Authors and Affiliations

  1. Institute for Mathematical Modeling, RAS, Moscow, Russia

    V. F. Kovalev

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  1. V. F. Kovalev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 405–418, June, 1999.

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Kovalev, V.F. Renormalization group analysis for singularities in the wave beam self-focusing problem. Theor Math Phys 119, 719–730 (1999). https://doi.org/10.1007/BF02557382

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