On spatial Fourier spectrum of rogue wave breathers

TL;DR

This paper derives exact analytical expressions for the spatial Fourier spectrum of breather solutions to the nonlinear Schrödinger equation, which are models for rogue waves, revealing spectrum characteristics based on spatial-temporal periodicity.

Contribution

It provides the first explicit formulas for the Fourier spectrum of rogue wave breather solutions, clarifying their spectral properties under different periodicity conditions.

Findings

Exact formulas for the Fourier spectrum of breather solutions.

Spectrum characteristics depend on spatial-temporal periodicity.

Continuous or discrete spectrum features identified.

Abstract

In this article, we derive exact analytical expressions for the spatial Fourier spectrum of the soliton family on a constant background. Also known as breathers, these solitons are exact solutions of the nonlinear Schr\"odinger equation and are considered as prototypes for rogue wave models. Depending on the periodicity in the spatial-temporal domain, the characteristics in the wavenumber-temporal domain may feature either a continuous or discrete spectrum.