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

Abstract

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the selfmodulation 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 superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

“…(3). This is consistent with the consensus that Rogue Waves are a generic phenomenon of nonlinear dispersive waves Dudley et al 2014;He et al 2014;Kibler et al 2015;Onorato et al 2013b), and thus, they do not originate from some peculiar term arising only in a very specific context.…”

“…Indeed, the mathematical study of focusing Schrödinger equations with non-vanishing behaviour at infinity indicates that it is much more unstable than the vanishing case, and this aspect seems to play a role in the formation of Rogue Waves. One realization of this effect is the formation of breathers, long linked with Rogue Waves (Chabchoub et al 2012;Dudley et al 2014;Kibler et al 2015;Onorato et al 2013). However, breathers grow out of a plane wave background; the object of our analysis is to capture the first stages of a breather-like solution growing out of a background consistent with a realistic Fourier spectrum, in particular not an exact plane wave.…”

“…Numerous studies link them with breathers (Chabchoub et al 2012;Dudley et al 2014;Kibler et al 2015;Onorato et al 2013) or other special solutions of nonlinear Schrödinger equations.…”

“…Many authors point out that Benjamin-Feir instabilities of focusing nonlinear waves must play a key role in the formation of Rogue Waves Kibler et al 2015;Onorato et al 2013b). In this work, we quantify for the first time how a continuous superposition of BenjaminFeir-type instabilities can create a highly localized, rapidly growing perturbation of a noisy wave background.…”

Formation of rogue waves from a locally perturbed condensate

“…In our previous works [15,22,23,37] we use Joukowsky transform (uniformization) of standard spectral parameter λ to simplify analysis of N -breather solutions:…”