Characteristic triangular spectra of extreme localised structures: insight from optics into rogue wave early warning

In this paper, we discuss a complementary indicator of rogue wave presence and show that information on the presence of rogue wave structures can in fact also be contained in the shape of the spectrum of the propagating field. In particular, we show that large classes of rational localized soliton solutions to the nonlinear Schrodinger equation (NLSE) are associated with a characteristic triangular spectrum when measured (as is commonly the case) on a logarithmic scale. The presence of such log-triangular structure has already been associated with Akhmediev breather localization in the early stage of supercontinuum generation, and the results here generalize this to a wider class of solution.