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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

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

This article is cited 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.

UDC: 517.957

MSC: 35Q53

Received: 28.04.2011
Revised: 23.06.2011



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