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Teoreticheskaya i Matematicheskaya Fizika, 1990, Volume 84, Number 2, Pages 163–172 (Mi tmf5870)  

This article is cited in 11 scientific papers (total in 11 papers)

Modulation instability of solutions of the nonlinear Schrödinger equation

G. L. Alfimov, A. R. Its, N. E. Kulagin
References:
Abstract: Multiphase solutions that describe the modulation instability of spatially periodic solutions of the nonlinear Schrödinger equation are constructed.
Received: 17.11.1988
English version:
Theoretical and Mathematical Physics, 1990, Volume 84, Issue 2, Pages 787–793
DOI: https://doi.org/10.1007/BF01017675
Bibliographic databases:
Language: Russian
Citation: G. L. Alfimov, A. R. Its, N. E. Kulagin, “Modulation instability of solutions of the nonlinear Schrödinger equation”, TMF, 84:2 (1990), 163–172; Theoret. and Math. Phys., 84:2 (1990), 787–793
Citation in format AMSBIB
\Bibitem{AlfItsKul90}
\by G.~L.~Alfimov, A.~R.~Its, N.~E.~Kulagin
\paper Modulation instability of~solutions of~the nonlinear Schr\"odinger equation
\jour TMF
\yr 1990
\vol 84
\issue 2
\pages 163--172
\mathnet{http://mi.mathnet.ru/tmf5870}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1077808}
\zmath{https://zbmath.org/?q=an:0718.35088}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 84
\issue 2
\pages 787--793
\crossref{https://doi.org/10.1007/BF01017675}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990FD70200001}
Linking options:
  • https://www.mathnet.ru/eng/tmf5870
  • https://www.mathnet.ru/eng/tmf/v84/i2/p163
  • This publication is cited in the following 11 articles:
    1. W.A. Clarke, R. Marangell, “Rigorous justification of the Whitham modulation theory for equations of NLS type”, Stud Appl Math, 147:2 (2021), 577  crossref
    2. A. B. Yakhshimuratov, “Integration of a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions”, Theoret. and Math. Phys., 202:2 (2020), 137–149  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Smirnov A.O., Gerdjikov V.S., Matveev V.B., “From Generalized Fourier Transforms to Spectral Curves For the Manakov Hierarchy. II. Spectral Curves For the Manakov Hierarchy”, Eur. Phys. J. Plus, 135:7 (2020), 561  crossref  isi
    4. Matveev V.B., Smirnov A.O., “Akns and Nls Hierarchies, Mrw Solutions, P-N Breathers, and Beyond”, J. Math. Phys., 59:9, SI (2018), 091419  crossref  mathscinet  zmath  isi  scopus
    5. V. B. Matveev, A. O. Smirnov, “Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach”, Theoret. and Math. Phys., 186:2 (2016), 156–182  mathnet  crossref  crossref  mathscinet  isi  elib
    6. D. J. Kedziora, A. Ankiewicz, A. Chowdury, N. Akhmediev, “Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25:10 (2015)  crossref
    7. Yakhshimuratov A., “The Nonlinear Schrodinger Equation with a Self-consistent Source in the Class of Periodic Functions”, Math Phys Anal Geom, 14:2 (2011), 153–169  crossref  isi
    8. Camus G. Latchio Tiofack, Alidou Mohamadou, Timoléon C. Kofané, Alain B. Moubissi, “Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg-Landau equation”, Phys. Rev. E, 80:6 (2009)  crossref
    9. R. Ganapathy, Boris A. Malomed, K. Porsezian, “Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers”, Physics Letters A, 354:5-6 (2006), 366  crossref
    10. Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271  crossref  mathscinet  zmath  isi
    11. Fritz Gesztesy, Rudi Weikard, “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”, Acta Math., 181:1 (1998), 63  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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