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Teoreticheskaya i Matematicheskaya Fizika, 1986, Volume 69, Number 2, Pages 189–194 (Mi tmf5217)  
This article is cited in 714 scientific papers (total in 714 papers)

Modulation instability and periodic solutions of the nonlinear Schrödinger equation

N. N. Akhmediev, V. I. Korneev
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Abstract: A very simple exact analytic solution of the nonlinear Schrödinger equation is found in the class of periodic solutions. It describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed. Expressions are obtained for the evolution of the spectrum of this solution, and these expressions are analyzed qualitatively. It is shown that there exists a certain class of periodic solutions for which the real and imaginary parts are linearly related, and an example of a one-parameter family of such solutions is given.
Received: 23.07.1985
English version:
Theoretical and Mathematical Physics, 1986, Volume 69, Issue 2, Pages 1089–1093
DOI: https://doi.org/10.1007/BF01037866
Bibliographic databases:
Language: Russian
Citation: N. N. Akhmediev, V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation”, TMF, 69:2 (1986), 189–194; Theoret. and Math. Phys., 69:2 (1986), 1089–1093
Citation in format AMSBIB
\Bibitem{AkhKor86}
\by N.~N.~Akhmediev, V.~I.~Korneev
\paper Modulation instability and periodic solutions of the nonlinear Schr\"odinger equation
\jour TMF
\yr 1986
\vol 69
\issue 2
\pages 189--194
\mathnet{http://mi.mathnet.ru/tmf5217}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=884491}
\zmath{https://zbmath.org/?q=an:0625.35015}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 69
\issue 2
\pages 1089--1093
\crossref{https://doi.org/10.1007/BF01037866}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986J382700003}
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    • This publication is cited in the following 714 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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