On spatial Fourier spectrum of rogue wave breathers

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 Schrodinger 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.