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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 62–66 (Mi timm808)  

This article is cited in 1 scientific paper (total in 1 paper)

Autoresonance excitation of a soliton of the nonlinear Schrödinger equation

R. N. Garifullin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: The action of an external parametric perturbation with slowly changing frequency on a soliton of the nonlinear Schrödinger equation is studied. Equations for the time evolution of the parameters of the perturbed soliton are derived. Conditions for the soliton phase locking are found, which relate the rate of change of the perturbation frequency, its amplitude, the wave number, and the phase to the initial data of the soliton. The cases when the initial amplitude of the soliton is small and when the amplitude of the soliton is of the order of unity are considered.

Keywords: autoresonance, perturbation, nonlinear Schrödinger equation, soliton.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 281, suppl. 1, 59–63

Bibliographic databases:

Document Type: Article
UDC: 517.955.8
Received: 28.09.2011

Citation: R. N. Garifullin, “Autoresonance excitation of a soliton of the nonlinear Schrödinger equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 62–66; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 59–63

Citation in format AMSBIB
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\by R.~N.~Garifullin
\paper Autoresonance excitation of a~soliton of the nonlinear Schr\"odinger equation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 62--66
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 281
\issue , suppl. 1
\pages 59--63
\crossref{https://doi.org/10.1134/S0081543813050064}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84879131621}


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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. O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84  mathnet  crossref  mathscinet  isi  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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