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 TMF, 2003, Volume 135, Number 1, Pages 107–116 (Mi tmf179)

Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode

I. O. Zolotovskii, D. I. Sementsov

Ulyanovsk State University

Abstract: We investigate the dynamics of the wave packet formed by two codirected strongly interacting waves propagating in a medium with cubic nonlinearity. We obtain a soliton solution of the nonlinear Schrödinger equation in the degenerate case where the wave packet is described by a single partial momentum. In the nondegenerate case, we use the variational method to find the equation for the pulse duration, which turns out to be analogous to the equation for the coordinate in the Kepler problem. Solving it, we find the dependences of the pulse duration on the propagation distance in the cases of “finite” and “infinite” propagation regimes.

Keywords: wave packet, partial momentum, soliton solution, compression

DOI: https://doi.org/10.4213/tmf179

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English version:
Theoretical and Mathematical Physics, 2003, 135:1, 541–548

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Revised: 17.04.2002

Citation: I. O. Zolotovskii, D. I. Sementsov, “Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode”, TMF, 135:1 (2003), 107–116; Theoret. and Math. Phys., 135:1 (2003), 541–548

Citation in format AMSBIB
\Bibitem{ZolSem03} \by I.~O.~Zolotovskii, D.~I.~Sementsov \paper Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode \jour TMF \yr 2003 \vol 135 \issue 1 \pages 107--116 \mathnet{http://mi.mathnet.ru/tmf179} \crossref{https://doi.org/10.4213/tmf179} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1997653} \zmath{https://zbmath.org/?q=an:1178.78015} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 135 \issue 1 \pages 541--548 \crossref{https://doi.org/10.1023/A:1023239603962} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183054500006} 

• http://mi.mathnet.ru/eng/tmf179
• https://doi.org/10.4213/tmf179
• http://mi.mathnet.ru/eng/tmf/v135/i1/p107

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Adamova, MS, “Control of the pulse dynamics in a two-mode nonlinear optical guide with strong intermode coupling”, Journal of Communications Technology and Electronics, 52:5 (2007), 573
2. Zolotovskii, IO, “Optical radiation dynamics in optical fibers with nonlinear intermode coupling”, Optics and Spectroscopy, 107:1 (2009), 117
3. Adamova, MS, “Nonlinear dynamics of optical pulses in fibres with a travelling refractive-index-change wave”, Quantum Electronics, 39:3 (2009), 256
4. Adamova, MS, “Dynamics of optical radiation in an optical waveguide with a time- and length-modulated refractive index”, Journal of Communications Technology and Electronics, 54:2 (2009), 197
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