Modulation instability—rogue wave correspondence hidden in integrable systems

The bulk-boundary correspondence is a key feature of topological physics and is universally applicable to Hermitian and non-Hermitian systems. Here, we report a similar universal correspondence intended for the rogue waves in integrable systems, by establishing the relationship between the fundamental rogue wave solutions of integrable models and the baseband modulation instability of continuous-wave backgrounds. We employ an N-component generalized nonlinear Schrödinger equation framework to exemplify this modulation instability-rogue wave correspondence, where we numerically confirm the excitation of three coexisting Peregrine solitons from a turbulent wave field, as predicted by the modulation instability analysis. The universality of such modulation instability-rogue wave correspondence has been corroborated using various integrable models, thereby offering an alternative way of obtaining exact rogue wave solutions from the modulation instability analysis.