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

2011, Vol. 7, No. 2, pp.  239-256

Author(s): Smirnov A. O., Golovachev G. M., Amosenok E. G.

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 $(n \leqslant 3)$. 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
Citation: Smirnov A. O., Golovachev G. M., Amosenok E. G., Two-gap 3-elliptic solutions of the Boussinesq and the Korteweg-de Vries equations, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 2, pp.  239-256
DOI:10.20537/nd1102004