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Nelin. Dinam., 2013, Volume 9, Number 3, Pages 389–407 (Mi nd396)  

This article is cited in 4 scientific papers (total in 4 papers)

Constructed in the elliptic functions three-phase solutions for the nonlinear Schrödinger equation

Alexander O. Smirnov, Grigory M. Golovachev

Saint Petersburg State University of Airspace Instrumentation (SUAI), Bolshaya Morskaya str. 67, Saint Petersburg, 190000, Russia

Abstract: Three-phase finite-gap with behavior of almost-periodic freak waves solutions for the nonlinear Schrödinger and the KP-I equations were constructed. Dependencies of parameters of solutions from the parameters of spectral curve were studied.

Keywords: rogue waves, freak waves, nonlinear Schrödinger equation, KP equation, Hirota equation, theta-function, reduction, covering.

Full text: PDF file (1018 kB)
References: PDF file   HTML file
UDC: 517.957
MSC: 35Q53
Received: 03.03.2013
Revised: 31.05.2013

Citation: Alexander O. Smirnov, Grigory M. Golovachev, “Constructed in the elliptic functions three-phase solutions for the nonlinear Schrödinger equation”, Nelin. Dinam., 9:3 (2013), 389–407

Citation in format AMSBIB
\Bibitem{SmiGol13}
\by Alexander~O.~Smirnov, Grigory~M.~Golovachev
\paper Constructed in the elliptic functions three-phase solutions for the nonlinear Schr\"odinger equation
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 3
\pages 389--407
\mathnet{http://mi.mathnet.ru/nd396}


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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. A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Trans. Moscow Math. Soc., 75 (2014), 173–183  mathnet  crossref  elib
    2. V. B. Matveev, F. Dyubard, A. O. Smirnov, “Kvaziratsionalnye resheniya nelineinogo uravneniya Shrëdingera”, Nelineinaya dinam., 11:2 (2015), 219–240  mathnet
    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. V. B. Matveev, A. O. Smirnov, “AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond”, J. Math. Phys., 59:9, SI (2018), 091419  crossref  mathscinet  zmath  isi  scopus
  • Нелинейная динамика
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