A collapse, i.e., the formation of regions with anomalously strong fields can take place in media with instantaneously relaxing cubic nonlinearity of dielectric permittivity. To describe the fields in such media, we use the nonlinear parabolic equation. The paper studies the behavior of the field near the singularity. The main idea of the work is the statement that the behavior of the field near the singularity depends on the field in the wings of the beam. It is shown that the differences in the behavior of the field near the focal point, which were found by various authors, are explained by different assumptions about the behavior of the field outside the collapsing part of the beam.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 1, pp. 63–72, January 2009.
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Vlasov, S.N. Influence of the peripheral field on the structure of a nonlinear focus arising during the propagation of a wave beam in a medium with cubic nonlinearity. Radiophys Quantum El 52, 57–66 (2009). https://doi.org/10.1007/s11141-009-9105-3
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DOI: https://doi.org/10.1007/s11141-009-9105-3