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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 119, Number 3, Pages 405–418
DOI: https://doi.org/10.4213/tmf748 (Mi tmf748) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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

V. F. Kovalev

Institute for Mathematical Modelling, Russian Academy of Sciences
Full-text PDF (234 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf748
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.
Received: 13.10.1998
English version:
Theoretical and Mathematical Physics, 1999, Volume 119, Issue 3, Pages 719–730
DOI: https://doi.org/10.1007/BF02557382
Bibliographic databases:
Language: Russian
Citation: V. F. Kovalev, “Renormalization group analysis for singularities in the wave beam self-focusing problem”, TMF, 119:3 (1999), 405–418; Theoret. and Math. Phys., 119:3 (1999), 719–730
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 119
\issue 3
\pages 719--730
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  • https://www.mathnet.ru/eng/tmf/v119/i3/p405
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:46
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