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SIGMA 11 (2015), 032, 14 pages arXiv:1412.1562
https://doi.org/10.3842/SIGMA.2015.032
Three-Phase Freak Waves
Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov and Elena G. Semenova
St.-Petersburg State University of Aerospace Instrumentation (SUAI), 67 Bolshaya Morskaya Str., St.-Petersburg, 190000, Russia
Received December 05, 2014, in final form April 11, 2015; Published online April 21, 2015
Abstract
In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schrödinger equation and Kadomtsev-Petviashvili and Hirota equations that exhibit the behavior of almost-periodic ''freak waves''. We also study the dependency of the solution parameters on the spectral curves.
Key words:
nonlinear Schrödinger equation; Hirota equation; freak waves; theta function; reduction; covering; spectral curve.
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