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Nelin. Dinam., 2011, Volume 7, Number 2, Pages 239–256 (Mi nd257)  

This article is cited in 3 scientific papers (total in 3 papers)

Two-gap 3-elliptic solutions of the Boussinesq and the Korteweg–de Vries equations

A. O. Smirnov, G. M. Golovachev, E. G. Amosenok

Saint Petersburg State University of Airspace Instrumentation (SUAI)

Abstract: The behavior of the two-gap elliptic solutions of the Boussinesq and the KdV equations was examined. These solutions were constructed by the $n$-sheet covering over a torus ($n\leqslant3$). It was shown that the shape of the two-gap elliptic solutions depends on $n$ and doesn't depend on the kind of the nonlinear wave equation.

Keywords: soliton, Boussinesq equation, KdV equation, theta-function, reduction, covering.

Full text: PDF file (4063 kB)
References: PDF file   HTML file
UDC: 517.957
MSC: 35Q53
Received: 28.04.2011
Revised: 23.06.2011

Citation: A. O. Smirnov, G. M. Golovachev, E. G. Amosenok, “Two-gap 3-elliptic solutions of the Boussinesq and the Korteweg–de Vries equations”, Nelin. Dinam., 7:2 (2011), 239–256

Citation in format AMSBIB
\Bibitem{SmiGolAmo11}
\by A.~O.~Smirnov, G.~M.~Golovachev, E.~G.~Amosenok
\paper Two-gap 3-elliptic solutions of the Boussinesq and the Korteweg--de~Vries equations
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 2
\pages 239--256
\mathnet{http://mi.mathnet.ru/nd257}
\elib{http://elibrary.ru/item.asp?id=16515648}


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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. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, Theoret. and Math. Phys., 173:1 (2012), 1403–1416  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. A. O. Smirnov, “Periodic Two-Phase “Rogue Waves””, Math. Notes, 94:6 (2013), 897–907  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407  mathnet
  • Нелинейная динамика
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