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2013
Impact Factor

    Grigory Golovachev

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

    Publications:

    Smirnov A. O., Golovachev G. M.
    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
    Citation: Smirnov A. O., Golovachev G. M.,  Constructed in the elliptic functions three-phase solutions for the nonlinear Schrödinger equation, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 3, pp.  389-407
    DOI:10.20537/nd1303001
    Smirnov A. O., Golovachev G. M., Amosenok E. G.
    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 $(n \leqslant 3)$. 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

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