Rogue wave spectra of the Sasa–Satsuma equation

•The rogue wave spectra of the Sasa–Satsuma equation are analyzed.•Numerical modeling of chaotic wave field according to this equation shows occasional generation of rogue waves.•The spectra of the chaotic wave fields have a triangular shape with significant widening when the rogue wave appears.•These spectra could be used for rogue wave detection.

We analyze the rogue wave spectra of the Sasa–Satsuma equation and their appearance in the spectra of chaotic wave fields produced through modulation instability. Chaotic wave fields occasionally produce high peaks that result in a wide triangular spectrum, which could be used for rogue wave detection.