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Mat. Zametki, 2013, Volume 94, Issue 6, Pages 871–883 (Mi mz9343)  

This article is cited in 6 scientific papers (total in 6 papers)

Periodic Two-Phase “Rogue Waves”

A. O. Smirnov

Saint-Petersburg State University of Aerospace Instrumentation

Abstract: A family of periodic (in $x$ and $z$) two-gap solutions of the focusing nonlinear Schrödinger equation is constructed. A condition under which the two-gap solutions exhibit the behavior of periodic “rogue waves” is obtained.

Keywords: focusing nonlinear Schrödinger equation, “rogue wave,” periodic two-gap solution, multiphase solution, finite-gap integration, cycle basis, amplitude peak.

DOI: https://doi.org/10.4213/mzm9343

Full text: PDF file (1140 kB)
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English version:
Mathematical Notes, 2013, 94:6, 897–907

Bibliographic databases:

UDC: 517.957
Received: 24.04.2012
Revised: 16.01.2013

Citation: A. O. Smirnov, “Periodic Two-Phase “Rogue Waves””, Mat. Zametki, 94:6 (2013), 871–883; Math. Notes, 94:6 (2013), 897–907

Citation in format AMSBIB
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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. Ch. Chabalko, A. Moitra, B. Balachandran, “Rogue waves: New forms enabled by GPU computing”, Phys. Lett. A, 378:32-33 (2014), 2377–2381  crossref  zmath  adsnasa  isi
    2. Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova, “Three-Phase Freak Waves”, SIGMA, 11 (2015), 032, 14 pp.  mathnet  crossref  mathscinet
    3. 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  adsnasa  isi  elib
    4. A. O. Smirnov, V. B. Matveev, “Dvukhfaznye periodicheskie resheniya uravnenii iz AKNS ierarkhii”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 205–227  mathnet
    5. M. Kamalian, A. Vasylchenkova, D. Shepelsky, J. E. Prilepsky, S. K. Turitsyn, “Signal modulation and processing in nonlinear fibre channels by employing the Riemann-Hilbert problem”, J. Lightwave Technol., 36:24 (2018), 5714–5727  crossref  isi  scopus
    6. P. G. Grinevich, P. M. Santini, “The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1”, Nonlinearity, 31:11 (2018), 5258–5308  crossref  mathscinet  isi  scopus
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