<p>It is known that the modulation instability (MI) is a focusing mechanism responsible for the formation of rogue waves (RWs). Such dynamics are initiated from the injection of sidebands, which translates into an amplitude modulation (AM) of the wave field. The nonlinear stage of unstable wave evolution can be described by exact breather solutions of the nonlinear Schrödinger equation (NLSE). In fact, the amplitude modulation of such coherent RW structures is connected to a particular phase-shift seeded in the carrier wave, i.e. a particular form of localized frequency modulation (FM). By seeding only the local FM information of a deterministic breather to a regular wave train, our experiments show that such an FM localization can indeed trigger pure breather-type RW dynamics. Results of an experimental study on identifying spontaneous RWs in a random wave field by isolating the respective FM and AM dynamics will also be discussed. </p>

As a result of integrability a variety of steady and pulsating solution have been derived [16,17]. We will not recall the parametrization of three fundamental breathers on a finite-amplitude carrier as these have been discussed in many past publications [18][19][20][21]. The family of ABs describe the nonlinear stage of MI and are periodic in time

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