Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superre…