Observation of modulation instability and rogue breathers on stationary periodic waves

TL;DR

This paper reports the first experimental observation of modulation instability and rogue breathers on stationary periodic waves like cnoidal and dnoidal envelopes in nonlinear optics and hydrodynamics, confirming their stability and dynamics.

Contribution

It provides the first experimental validation of modulation instability and rogue breather formation on stationary periodic background waves, extending understanding beyond fundamental plane waves.

Findings

Quantitative measurements of modulation instability gain.

Observation of rogue breather solutions induced by perturbations.

Confirmation of modulation instability on complex periodic backgrounds.

Abstract

We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known solutions of the nonlinear Schrodinger equation, the stability of such background waves has remained unexplored experimentally until now, unlike the fundamental plane wave. By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we report on quantitative measurements of spontaneous modulation instability gain seeded by input random noise, as well as the formation of rogue breather solutions induced by a coherent perturbation. Our results confirm the generalization of modulation instability when more complex background waves are involved.