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TMF, 1997, Volume 111, Number 3, Pages 369–388 (Mi tmf1015)  

This article is cited in 9 scientific papers (total in 9 papers)

Renormgroup symmetries in problems of nonlinear geometrical optics

V. F. Kovalev

Institute for Mathematical Modelling, Russian Academy of Sciences

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.

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

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English version:
Theoretical and Mathematical Physics, 1997, 111:3, 686–702

Bibliographic databases:

Received: 06.02.1997

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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\paper Renormgroup symmetries in problems of nonlinear geometrical optics
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\jour Theoret. and Math. Phys.
\yr 1997
\vol 111
\issue 3
\pages 686--702
\crossref{https://doi.org/10.1007/BF02634057}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Kovalev, “Renormalization group analysis for singularities in the wave beam self-focusing problem”, Theoret. and Math. Phys., 119:3 (1999), 719–730  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Kovalev V.F., “Computer algebra tools in construction of renormgroup symmetries”, Casc'99: Computer Algebra in Scientific Computing, 1999, 251–267  crossref  mathscinet  zmath  isi
    4. Kovalev, VF, “Approximate transformation groups and renormgroup symmetries”, Nonlinear Dynamics, 22:1 (2000), 73  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Kovalev, VF, “Renormalization-group approach to the problem of light-beam self-focusing”, Physical Review A, 61:3 (2000), 033809  crossref  mathscinet  adsnasa  isi  scopus  scopus
    6. Shirkov, DV, “The Bogoliubov renormalization group and solution symmetry in mathematical physics”, Physics Reports-Review Section of Physics Letters, 352:4–6 (2001), 219  crossref  mathscinet  zmath  isi  scopus  scopus
    7. V. F. Kovalev, D. V. Shirkov, “Renormalization-group symmetries for solutions of nonlinear boundary value problems”, Phys. Usp., 51:8 (2008), 815–830  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    8. Tatarinova, LL, “Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics”, Physical Review A, 78:2 (2008), 021806  crossref  adsnasa  isi  elib  scopus  scopus
    9. 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  crossref  zmath  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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