Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova, “Three-Phase Freak Waves”, SIGMA, 2015, Volume 11,032, 14 pp.

This article is cited in 4 papers

Three-Phase Freak Waves

Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova

St.-Petersburg State University of Aerospace Instrumentation (SUAI), 67 Bolshaya Morskaya Str., St.-Petersburg, 190000, Russia

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.

Keywords: nonlinear Schrödinger equation; Hirota equation; freak waves; theta function; reduction; covering; spectral curve.

MSC: 35Q55; 37C55

Received: December 5, 2014; in final form April 11, 2015; Published online April 21, 2015

Language: English

DOI: 10.3842/SIGMA.2015.032