Extreme waves that appear from nowhere: On the nature of rogue waves

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

“…We report here a novel optical fiber-based test bed using tailored modulated initial conditions of a continuous wave to excite the formation of two Akhmediev breathers (ABs) that collide during propagation. Our experimental work confirms the analytical predictions of breather collision by Akhmediev et al [7,26]. We have also investigated the synchronization of the collision by controlling the phase and velocity differences between ABs.…”

“…These coherent localized waves evolving on a continuous background exactly describe the dynamical growth of perturbations on a continuous wave related to the nonlinear modulation instability. This includes Akhmediev breathers, Kuznetsov-Ma solitons, and the Peregrine (rational) soliton, which are now considered the simplest models to describe the growth and decay of isolated steep wave events, i.e., rogue waves, in nonlinear dispersive systems [5][6][7][8][9]. But although their first observations were confirmed in different domains of nonlinear science over the past few years, including hydrodynamics [10] and plasma physics [11], no experiment has been performed in order to reveal a synchronized interaction between these first-order periodic solutions of the NLSE.…”

“…Even in the presence of phase randomization inherent to the study of incoherent waves or chaotic states, various numerical works have shown the spontaneous emergence of coherent localized waves (even rational solutions of the NLSE) from a turbulent environment [7,[13][14][15]. Rogue waves are not just an offshoot of breather collisions, but other mechanisms depending on the physical system must be taken into account in the formation of rogue waves, including the statistical approach, when noise is present [16].…”

“…These doubly localized waves have been generated in a water-wave tank through nonlinear focusing of initial modulated waves derived from their analytic solutions. However, these higher-order solutions can be interpreted as a nonlinear superposition of two or more rational solutions of first order [7]. As an alternative to describing giant waves, one can consider the collision of first-order periodic solutions of the NLSE theoretically studied in Ref.…”

“…As an alternative to describing giant waves, one can consider the collision of first-order periodic solutions of the NLSE theoretically studied in Ref. [7]. Collision between emerging breather structures from waves undergoing modulation instability also appears to be a precursor to the formation of rogue soliton pulses in the process of supercontinuum generation [22].…”