Modulation instability—rogue wave correspondence hidden in integrable systems

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