### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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