Bolshaya Morskaya st., 67, Saint Petersburg, 190000, Russia
Saint Petersburg State University of Airspace Instrumentation (SUAI)
Matveev V. B., Dubard P., Smirnov A. O.
Quasi-rational solutions of nonlinear Schrodinger equation
2015, Vol. 11, No. 2, pp. 219-240
The method for constructing quasi-rational solutions of the nonlinear Schrödinger equation, Kadomtsev–Petviashvili equation and some other integrable nonlinear equations is considered. Examples of range 2 and 3 solutions are given.
Smirnov A. O., Golovachev G. M.
Constructed in the elliptic functions three-phase solutions for the nonlinear Schrödinger equation
2013, Vol. 9, No. 3, pp. 389-407
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.
Smirnov A. O., Golovachev G. M., Amosenok E. G.
Two-gap 3-elliptic solutions of the Boussinesq and the Korteweg-de Vries equations
2011, Vol. 7, No. 2, pp. 239-256
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.