V. F. Kovalev, “Renormgroup symmetries in problems of nonlinear geometrical optics”, TMF, 111:3 (1997), 369–388; Theoret. and Math. Phys., 111:3 (1997), 686

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 111, Number 3, Pages 369–388
DOI: https://doi.org/10.4213/tmf1015 (Mi tmf1015)

This article is cited in 10 scientific papers (total in 10 papers)

Renormgroup symmetries in problems of nonlinear geometrical optics

V. F. Kovalev

Institute for Mathematical Modelling, Russian Academy of Sciences

Full-text PDF (311 kB) Citations (10)

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DOI: https://doi.org/10.4213/tmf1015

Abstract: Renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation are constructed. With the help of renormgroup symmetries new exact and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of a laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium.

Received: 06.02.1997

English version:
Theoretical and Mathematical Physics, 1997, Volume 111, Issue 3, Pages 686–702
DOI: https://doi.org/10.1007/BF02634057

Bibliographic databases:

Language: Russian

Citation: V. F. Kovalev, “Renormgroup symmetries in problems of nonlinear geometrical optics”, TMF, 111:3 (1997), 369–388; Theoret. and Math. Phys., 111:3 (1997), 686–702

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1015

https://doi.org/10.4213/tmf1015

https://www.mathnet.ru/eng/tmf/v111/i3/p369

This publication is cited in the following 10 articles:

Tatarinova L.L., Garcia M.E., “Light propagation in media with a highly nonlinear response: An analytical study”, Physica D-Nonlinear Phenomena, 240:9–10 (2011), 894–901
M. E. Garcia, V. F. Kovalev, L. L. Tatarinova, “Exact and approximate symmetries for light propagation equations with higher order nonlinearity”, Lobachevskii J Math, 31:2 (2010), 123
V. F. Kovalev, D. V. Shirkov, “Renormalization-group symmetries for solutions of nonlinear boundary value problems”, Phys. Usp., 51:8 (2008), 815–830
Tatarinova, LL, “Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics”, Physical Review A, 78:2 (2008), 021806
Shirkov, DV, “The Bogoliubov renormalization group and solution symmetry in mathematical physics”, Physics Reports-Review Section of Physics Letters, 352:4–6 (2001), 219
Kovalev, VF, “Approximate transformation groups and renormgroup symmetries”, Nonlinear Dynamics, 22:1 (2000), 73
Kovalev, VF, “Renormalization-group approach to the problem of light-beam self-focusing”, Physical Review A, 61:3 (2000), 033809
V. F. Kovalev, “Renormalization group analysis for singularities in the wave beam self-focusing problem”, Theoret. and Math. Phys., 119:3 (1999), 719–730
V. F. Kovalev, D. V. Shirkov, “Functional self-similarity and renormalization group symmetry in mathematical physics”, Theoret. and Math. Phys., 121:1 (1999), 1315–1332
Kovalev V.F., “Computer algebra tools in construction of renormgroup symmetries”, Casc'99: Computer Algebra in Scientific Computing, 1999, 251–267

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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