Three-Phase Freak Waves

TL;DR

This paper introduces three-phase finite-gap solutions to several integrable equations, demonstrating their almost-periodic freak wave behavior and analyzing how solution parameters depend on spectral curves.

Contribution

It presents new three-phase finite-gap solutions for nonlinear equations, linking spectral curve properties to wave behaviors, advancing understanding of freak wave phenomena.

Findings

Demonstration of almost-periodic freak wave solutions

Analysis of parameter dependence on spectral curves

Extension of finite-gap solution methods to multiple equations

Abstract

In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schr\"odinger 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.