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.
Highlights
During the last decades, the modulation instability (MI) phenomenon has attracted a significant research interest in a variety of nearly conservative wave systems described by the nonlinear Schrödinger equation (NLSE) in its many forms [1,2,3,4,5,6,7,8,9,10,11,12]
We report an experimental study on the modulation instability process and associated rogue breathers for the case of stationary periodic background waves, namely dnoidal and cnoidal envelopes
By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we observe the spontaneous modulation instability gain seeded by input random noise and the formation of rogue breathers induced by a coherent perturbation
Summary
The modulation instability (MI) phenomenon has attracted a significant research interest in a variety of nearly conservative wave systems (water surface, plasmas, guided laser light, electrical transmission lines, and Bose–Einstein condensates) described by the nonlinear Schrödinger equation (NLSE) in its many forms [1,2,3,4,5,6,7,8,9,10,11,12] This includes the linear stability analysis of the plane waves and the subsequent nonlinear stage of MI, namely the formation of localized waves such as solitons and breathers, as well as multibreather complexes. In hydrodynamical experiments, we observe rogue breathers on both backgrounds of the dn waves and the cn waves; observation of MI gains from random noise is difficult due to the limitations imposed by the length of the wave facility
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