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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 10, Pages 1752–1773 (Mi zvmmf235)  
This article is cited in 2 scientific papers (total in 2 papers)

Conservative finite-difference scheme for the problem of a femtosecond laser pulse with an axially symmetric profile propagating in a medium with cubic nonlinearity

A. G. Volkov, V. A. Trofimov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
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Abstract: Conservative finite-difference schemes are constructed for the problem of a femtosecond laser pulse propagating in a cubically nonlinear medium in the axially symmetric case with allowance for temporal dispersion of the nonlinear response of the medium. The process is governed by the nonlinear Schrödinger equation involving the time derivative of the nonlinear term. The invariants of the differential problem are presented. It is shown that the difference analogues of these invariants hold for the solution to the finite-difference schemes proposed for the problem. As an example, the numerical results obtained for the self-focusing of a femtosecond light beam are presented.
Key words: femtosecond laser pulse, combined nonlinear Schrödinger equation, axially symmetric case, self-focusing, cubic nonlinearity.
Received: 27.03.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 10, Pages 1681–1701
DOI: https://doi.org/10.1134/S0965542507100090
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. G. Volkov, V. A. Trofimov, “Conservative finite-difference scheme for the problem of a femtosecond laser pulse with an axially symmetric profile propagating in a medium with cubic nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007), 1752–1773; Comput. Math. Math. Phys., 47:10 (2007), 1681–1701
Citation in format AMSBIB
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\by A.~G.~Volkov, V.~A.~Trofimov
\paper Conservative finite-difference scheme for the problem of a~femtosecond laser pulse with an axially symmetric profile propagating in a~medium with cubic nonlinearity
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 10
\pages 1752--1773
\mathnet{http://mi.mathnet.ru/zvmmf235}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2388625}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 10
\pages 1681--1701
\crossref{https://doi.org/10.1134/S0965542507100090}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35648973343}
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    • This publication is cited in the following 2 articles:
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