Abstract:
Functional self-similarity one-dimensional inhomogeneous electron plasma under the influence of intensive electro-magnetic radiation is demonstrated. Using the group transformation of the results of the perturbation theory in the nonlinearity parameter, we find the exact and renormalization group solutions for the nonlinear structure of the electromagnetic field and analyze its spectral contents.
Citation:
V. F. Kovalev, V. V. Pustovalov, “Functional self-similarity in a problem of plasma theory with electron nonlinearity”, TMF, 81:1 (1989), 69–85; Theoret. and Math. Phys., 81:1 (1989), 1060–1071
\Bibitem{KovPus89}
\by V.~F.~Kovalev, V.~V.~Pustovalov
\paper Functional self-similarity in~a~problem of~plasma theory with electron nonlinearity
\jour TMF
\yr 1989
\vol 81
\issue 1
\pages 69--85
\mathnet{http://mi.mathnet.ru/tmf5267}
\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 81
\issue 1
\pages 1060--1071
\crossref{https://doi.org/10.1007/BF01015510}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1989DE07500007}
Linking options:
https://www.mathnet.ru/eng/tmf5267
https://www.mathnet.ru/eng/tmf/v81/i1/p69
This publication is cited in the following 18 articles:
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Relativistic-nonlinear resonant absorption and generation of harmonics of electromagnetic radiation in an inhomogeneous plasma”, Phys. Usp., 67:5 (2024), 429–463
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Nonlinear Laser Radiation Absorption Due to Relativistic Plasma Resonance in an Inhomogeneous Plasma”, J. Exp. Theor. Phys., 133:2 (2021), 236
I. I. Metelskii, “Relativistically Nonlinear Resonance Absorption at Small Incidence Angles of Laser Radiation on Inhomogeneous Plasma”, Bull. Lebedev Phys. Inst., 48:12 (2021), 400
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Harmonic Generation by Relativistic Plasma Resonance”, J Russ Laser Res, 40:5 (2019), 429
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Higher-order harmonic generation of laser radiation due to relativistic plasma resonance at nonrelativistic laser intensity”, Physics of Plasmas, 26:11 (2019)
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Nonlinear relativistic plasma resonance: Renormalization group approach”, Plasma Phys. Rep., 43:2 (2017), 175
I. I. Metelskii, V. F. Kovalev, V. Yu. Bychenkov, “Nonlinear plasma resonance in inhomogeneous relativistic plasma”, Bull. Lebedev Phys. Inst., 43:1 (2016), 16
I I Metelskii, V F Kovalev, V Yu Bychenkov, “Renormgroup algorithm for the theory of the relativistic plasma resonance”, J. Phys.: Conf. Ser., 769 (2016), 012083
Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 145
Nonlinear Physical Science, Approximate and Renormgroup Symmetries, 2009, 95
V. F. Kovalev, D. V. Shirkov, “Renormalization-group symmetries for solutions of nonlinear boundary value problems”, Phys. Usp., 51:8 (2008), 815–830
Kovalev, VF, “Renorm-group symmetry for functionals of boundary value problem solutions”, Journal of Physics A-Mathematical and General, 39:25 (2006), 8061
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, 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
Vladimir F. Kovalev, Computer Algebra in Scientific Computing CASC'99, 1999, 251
D. V. Shirkov, “The Bogolyubov renormalization group”, Russian Math. Surveys, 49:5 (1994), 155–176
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