Exact analytic spectra of rogue waves for Manakov equations

Abstract: The spectra of rogue waves of Manakov equations that exist in both focusing or defocusing regimes are derived in analytic form. These spectra are asymmetric during their whole expansion-contraction cycle. They have triangular shape at each side of the spectrum in the log scale. Such spectra are characterised by two quantities: the slopes of the spectra and the spectral jump at zero frequency. We confirm our analytical results using numerical simulations.