Observation of modulation instability and rogue breathers on stationary periodic waves

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.

References in corpus (3)

• Rogue waves and analogies in optics and oceanography
• The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
• Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band

Cited by in corpus (7)

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• Rogue waves in discrete-time quantum walks
• Rogue waves in quantum lattices with correlated disorder
• Trajectory control in idealized four-wave mixing processes in optical fiber
• Temporal localization of optical waves supported by a copropagating quasiperiodic structure
• Dissipation induced elastic-mode instability with topological excitation in holographic non-equilibrium steady cnoidal wave supersolid
• Forced symmetry breaking as a mechanism for rogue bursts in a dissipative nonlinear dynamical lattice