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Cellular automata are conceptual discrete dynamical systems useful in the theory of information. The spatiotemporal patterns that they produce are intimately related to computational mechanics in distributed complex systems. Here, we investigate their physical implementation in the framework of chimera states in which coherent and incoherent behavior coexist. Hence, chimera states were subject to quantitative and qualitative analyzes borrowing the same tools used to characterize cellular automata. Our results reveal the existence of cellular automata-type dynamics submerged in the dynamics exhibited by our optical chimera states. Thus, they share a panoply of attributes in terms of computational abilities.

Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal chaos and extreme events. However, the extensive feature of these evolutions constitutes a critical limitation for full-size forecasting processes. Hence, the main challenge for forecasting relevant events is to establish the set of pertinent information. Here, we identify precursors from the transfer entropy of the system and a deep Long Short-Term Memory network to forecast the complex dynamics of a system evolving in a high-dimensional spatiotemporal chaotic regime. Performances of this triggerable model-free prediction protocol based on the information flowing map are tested from experimental data originating from a passive resonator operating in such a complex nonlinear regime. We have been able to predict the occurrence of extreme events up to 9 round trips after the detection of precursor, i.e., 3 times the horizon provided by Lyapunov exponents, with 92 % of true positive predictions leading to 60 % of accuracy.

Predicting complex nonlinear dynamical systems has been even more urgent because of the emergence of extreme events such as earthquakes, volcanic eruptions, extreme weather events (lightning, hurricanes/cyclones, blizzards, tornadoes), and giant oceanic rogue waves, to mention a few. The recent milestones in the machine learning framework offer a new prospect in this area [1] , [2] . For a high dimensional chaotic system, increasing the system’s size causes an augmentation of the complexity and, finally, more nodes in the network. Here, we propose a new supervised machine learning strategy to forecast bursts occurring in the turbulent regime of a fiber ring cavity. Indeed, we have recently demonstrated [3] that this system can continuously transform a stable periodic pattern with a well-defined frequency comb into a turbulent state via a spatiotemporal intermittency mechanism. Figure 1a ) shows an illustration of this transition. Even though a turbulent evolutions, an interesting feature is the persistent long-range correlation in the dynamics [3] . The system can then be seen as adjacent subdomains. Owing to this feature, instead of predicting the whole system, we use appropriate tools of chaos theory to identify recurrent picture in the past at the same location of the bursts. Figure 1b ) shows the statistics on the bursts (red) and the profiles detected at a previously computed time lag (blue). We have taken advantage of the apparent causality to make an association precursors-pulses. Knowing when and where the bursts may emerge, a fair question is " What is coming? ". On the other hand, as shown in Figure 1c ), no correlation can be found between the profile (amplitude and size) of the precursors of the corresponding pulse. However, using the pulses/precursors pairs to perform supervised learning with a recurrent neural network, we have obtained a high correlated map between the actual observation and the prediction, as can be seen in Figure 1d ). As our strategy deals with intrinsic characteristic quantities of the dynamical behavior, the pre-trained network can trigger the forecasting even for a more extensive system, provided that all the other parameters are the same.

Pulsed pumping configurations are becoming an interesting scheme for triggering optical frequency combs (OFC) in passive resonators due to their high peak power and to their low induced thermal loading [1] . A careful change of the repetition rate of these pumps compared to the repetition rate of the resonators is required to get an efficient OFC generation. Small mismatches, cumulated over many round trips, can lead to significant drifts leading to crucial modifications of the dynamics of the processes. A deep investigation of the impact of the synchronization mismatch on the complex building-up of OFC has never been reported yet. Here, for simplicity, we first restricted our study to the impact of the synchronization mismatch on modulation instability, because MI is the first and simplest nonlinear phenomenon appearing in a passive resonator and involved in the formation of OFCs. In its basic formulation, MI phenomenon depends only on the even terms of the dispersion [1] . However, in the real world experimentation, it has been reported that under synchronous pumping, and in the weak dispersion regime, the slope of the dispersion leads the system to become convectively unstable inducing a power asymmetry between the side-bands [2] , [3] . Here we worked in a strong dispersion regime where these effects can be neglected. The cavity is pumped with square shape pulses with 560 ps duration, just above the MI threshold, (other parameters are listed in the figure’s caption). We recorded the output spectra with an optical spectrum analyzer and the round-trip to round-trip temporal evolution with a commercial time lens system (Picoluz). The evolution of the output spectra as a function of the synchronization mismatch is depicted in Fig. 1(a) . For perfect synchronization (ΔT=0), narrow MI sidebands are generated at 28.21 GHz (see inset), in pretty good agreement with theoretical predictions (40 GHz). Perfect synchronization operation is confirmed through the stable evolution of the pulse train round-trips over round -trips ( fig. 1(c) ). By slightly changing the synchronization mismatch of only a few tens of fs, the position of the sideband is shifted by more than 12 GHz. For large mismatch values (Mismatch> 0.01 ps/m), the positions of the sidebands are unchanged and they experience an important spectral broadening. This significant modification of the dynamics of the process is directly related to convective instabilities [2] , [3] associated with the synchronization mismatch as can be seen in Fig. 1(b) and (d) . Theoretically, it means that, the first order dispersion term (β 1 ) must be considered in the phase matching relation [2] , [3] .

We investigate the influence of the stimulated Raman scattering on the formation of bright and dark localized states in all-fiber resonators subject to a coherent optical injection, when operating in the normal dispersion regime. In the absence of the Raman effect, and far from any modulational instability, localized structures form due to the locking of domain walls connecting two coexisting continuous wave states, and undergo a particular bifurcation structure known as collapsed snaking. The stimulated Raman scattering breaks the reflection symmetry of the system, and modifies the dynamics, stability, and locking of domain walls. This modification leads to the formation of, not only dark, but also bright moving localized states, which otherwise are absent. We perform a detailed bifurcation analysis of these localized states, and classify their dynamics and stability as a function of the main parameters of the system.

A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato-Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures. This reduction is valid close to the nascent bistability regime, where the system undergoes a second-order critical point marking the onset of a hysteresis loop. The interaction between fronts allows for the stabilization of temporal localized structures. Without the Raman effect, moving temporal localized structures do not exist, as shown in M. G. Clerc, S. Coulibaly, and M. Tlidi, Phys. Rev. Res. 2, 013024 (2020). The detailed derivation of the speed and the width associated with these structures is presented. We characterize numerically in detail the bifurcation structure and stability associated with the moving temporal localized states. The numerical results of the governing equations are in close agreement with analytical predictions., SCOPUS: ar.j, info:eu-repo/semantics/published

We show analytically and numerically that time-delayed nonlocal response induces traveling localized states in bistable systems. These states result from the interaction of fronts between homogeneous steady states. We illustrate this mechanism by considering an experimentally relevant system - the fiber cavity with the noninstantaneous Raman response. Close to the nascent bistability, we performed a derivation of a generic bistable model with a nonlocal delayed response. Analytical expressions of the width and the speed of traveling localized states are derived. Without a time-delayed nonlocal response, traveling localized states are excluded. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation., SCOPUS: ar.j, info:eu-repo/semantics/published

We investigate spatiotemporal chaos dynamics in a finite nanoparticles array with Kerr-type nonlinear response, excited by an incident plane wave of varying intensity and tunable frequency close to the localized plasmon resonance of a single particle. Considering dipole-dipole coupling between the nanoparticles described by their polarizability, we compute the temporal evolution of the dipoles and numerically extract the Lyapunov spectra, allowing us to characterize different dynamical behaviors. Furthermore, we estimate the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. We show that time-modulated solutions which are generated at the onset of modulational instability experience secondary instabilities leading to a complex nonlinear dynamic. It is also shown that in the highly nonlinear regime, the spatiotemporal chaos is robust and exists in a large range of parameters that we have determined numerically.

Macroscopic systems are often subjected to time-delayed feedback. This effect is originated from temporal correlations that are inherent not only to optical and to magnetic systems, but also relevant to population dynamics where the birth rate includes the effect of maturation [1]. The delayed nonlocal response in nature is a rule rather than the exception.

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schr\"odinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength., Comment: 10 pages, 9 figures, Accepted

Arrays of oscillators driven out-of-equilibrium can support the coexistence between coherent and incoherent domains that have become known as chimera states. Recently, we have reported such an intriguing self-organization phenomenon in a chain of locally coupled Duffing oscillators. Based on this prototype model, we reveal a generalization of chimera states corresponding to the coexistence of incoherent domains. These freak states emerge through a bifurcation in which the coherent domain of an existing chimera state experiences an instability giving rise to another incoherent state. Using Lyapunov exponents and Fourier analysis allows us to characterize the dynamical nature of these extended solutions. Taking the Kuramoto order parameter, we were able to compute the bifurcation diagram of freak chimera states.

Two-dimensional arrays of coupled waveguides or coupled microcavities allow us to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence between a coherent and incoherent emission. In this regime, we show that two-dimensional chimera states can be generated. Depending on initial conditions, the system exhibits a family of two-dimensional chimera states and interaction between them. We characterize these two-dimensional structures by computing their Lyapunov spectrum and Yorke-Kaplan dimension. Finally, we show that two-dimensional chimera states are of spatiotemporal chaotic nature., SCOPUS: ar.j, info:eu-repo/semantics/published

Coupled nonlinear oscillators can present complex spatiotemporal behaviors. Here, we report the coexistence of coherent and incoherent domains, called chimera states, in an array of identical Duffing oscillators coupled to their nearest neighbors. The chimera states show a significant variation of amplitude in the desynchronized domain. These intriguing states are observed in the bistability region between a homogeneous state and a spatiotemporal chaotic one. These dynamical behaviors are characterized by their Lyapunov spectra and their global phase coherence order parameter. The local coupling between oscillators prevents one domain from invading the other one. Depending on initial conditions, a family of chimera states appear, organized in a snaking-like diagram.

Localized structures in optics have attracted attention for their potential applications in tele- communications and information storage. In the present work, localized structures with non-uniform phase structure in the degenerate optical parametrical oscillator are reported and elucidated. Dissipative solitons with non-uniform phase structures in parametrically driven systems have been already observed in prototype models being found in two typical shapes: symmetrical and asymmetrical. In contrast, the phase structure in degenerate optical parametrical oscillator is always symmetrical, showing a pro- nounced bell-shaped phase. We show that the nonlinear saturation present in this physical system is responsible of a relaxation dynamics and this symmetry. Probing that real physical systems exhibit al- ways this unique type of localized structure with phase structure. An adequate analytical description for the phase, based on a simple model, is achieved showing that such structure is controlled by the in- terplay between the detuning, the external pump and the losses of the cavity. Numerical simulations present quite agreement with theoretical predictions.

We study theoretically the primary and secondary instabilities undergone by the stationary periodic patterns in the Lugiato-Lefever equation in the focusing regime. Direct numerical simulations in a one-dimensional periodic domain show discrete changes of the periodicity of the patterns emerging from unstable homogeneous steady states. Through continuation methods of the steady states we reveal that the system exhibits a set of wave instability branches. The organisation of these branches suggests the existence of an Eckhaus scenario, which is characterized in detail by means of the derivation of their amplitude equation in the weakly nonlinear regime. The continuation in the highly nonlinear regime shows that the furthest branches become unstable through a Hopf bifurcation.

Supercontinuum generation results from the spectral broadening of an intense light arising from the interplay between several nonlinear optical effects. In this paper, a non-destructive optical time-domain reflectometry set-up is proposed to measure the spatial evolution of the spectral broadening induced along an optical fiber. The method is based on the measurement of the Rayleigh backscattered signals generated by the various components of the spectral broadening. The system was experimentally tested on conventional and highly nonlinear fibers. The experimental data obtained with the proposed method were in good agreement with the optical spectra measured by an optical spectrum analyzer at the fiber outputs. The proposed measurement method can be applied without damaging and/or perturbing the intrinsic dynamics of the supercontinuum generation.

We report the distributed measurement of supercontinnum generation along highly nonlinear optical fibers with centimeter spatial resolution using photon-counting optical time-domain reflectometry.

International audience; We analyze the exact Kuznetsov-Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov-Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kutzetsov-Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov-Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov-Ma soliton by a judicious choice of the amplitude and frequency of the modulation.

We propose a non-destructive measurement technique for the distributed measurement of supercontinuum generation in fibers. For validation purposes, we compare our results with those obtained thanks to the cut-back technique. A good agreement was observed.

We investigate the spatio-temporal dynamics of a ring cavity filled with a non-instantaneous Kerr medium and driven by a coherent injected beam. We show the existence of a stable mixed-mode solution that can be either extended or localized in space. The mixed-mode solutions are obtained in a regime where Turing instability (often called modulational instability) interacts with self-pulsing phenomenon (Andronov-Hopf bifurcation). We numerically describe the transition from stationary inhomogeneous solutions to a branch of mixed-mode solutions. We characterize this transition by constructing the bifurcation diagram associated with these solutions. Finally, we show stable localized mixed-mode solutions, which consist of time-periodic oscillations that are localized in space., 5 pages, 5 figures

The occurrence of extreme events in a spatially extended microcavity laser has been recently reported [Selmi et al., Phys. Rev. Lett. 116, 013901 (2016)] to be correlated to emergence of spatiotemporal chaos. In this dissipative system, the role of spatial coupling through diffraction is essential to observe the onset of spatiotemporal complexity. We investigate further the formation mechanism of extreme events by comparing the statistical and dynamical analyses. Experimental measurements together with numerical simulations allow us to assign the quasiperiodicity mechanism as the route to spatiotemporal chaos in this system. Moreover, by investigating the fine structure of the maximum Lyapunov exponent, of the Lyapunov spectrum, and of the Kaplan-Yorke dimension of the chaotic attractor, we are able to deduce that intermittency plays a key role in the proportion of extreme events measured. We assign the observed mechanism of generation of extreme events to quasiperiodic extended spatiotemporal intermittency.

Supercontinuum generation (SCG) in optical fibers arises from the spectral broadening of an intense light, which results from the interplay of both linear and nonlinear optical effects. In this Letter, a nondestructive optical time domain reflectometry method is proposed for the first time, to the best of our knowledge, to measure the spatial (longitudinal) evolution of the SC induced along an optical fiber. The method was experimentally tested on highly nonlinear fibers. The experimental results are in a good agreement with the optical spectra measured at the fiber outputs.

We consider coupled-waveguide resonators subject to optical injection. The dynamics of this simple device are described by the discrete Lugiato-Lefever equation. We show that chimera-like states can be stabilized, thanks to the discrete nature of the coupled-waveguide resonators. Such chaotic localized structures are unstable in the continuous Lugiato-Lefever model; this is because of dispersive radiation from the tails of localized structures in the form of two counter-propagating fronts between the homogeneous and the complex spatiotemporal state. We characterize the formation of chimera-like states by computing the Lyapunov spectra. We show that localized states have an intermittent spatiotemporal chaotic dynamical nature. These states are generated in a parameter regime characterized by a coexistence between a uniform steady state and a spatiotemporal intermittency state.

Nail Akhmediev et al. ; 38 págs.; 28 figs., The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of 'optical rogue waves'. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as 'an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses'. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1-4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms 'optical rogue waves' and 'extreme events' do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this 'roadmap' have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt. 15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research. © 2016 IOP Publishing, National Priority Research Program, project 6-021-1-005, of the Qatar National Research Fund. The work in China was supported by the National Natural Science Foundation of China under grant No. 61275001 and by the Natural Science Foundation of Guangdong Province, under Grant No. 2014A030313799. Australian Research Council (DE130101432, DP140100265 and DP150102057). The work of JMSC was supported by MINECO under contract TEC2012-37958-C02-02, and by C. A.M. under contract S2013/MIT-2790. JMSC and NA acknowledge the support of the Volkswagen Foundation Agence Nationale de la Recherche through projects ANR- 2010-BLANC-0417-01 and ANR-2012-BS04-001, the Région Bourgogne, and the Labex ACTION program ANR- 11-LABX-01-01. The work of JMSC was supported by MINECO under contract TEC2012-37958-C02-02, by C A M under contract S2013 / MIT-2790, and by the Volkswagen Foundation. French National Research Agency (Grant No. ANR-12- BS04-0011 OPTIROC), and the Labex ACTION (Grant No. ANR11-LABX-01-01). S R acknowledges FONDECYT grant N 1130709. Fond National de la Recherche Scientifique (FNRS), the Methusalem project and the Interuniversity Attraction 463 Poles program of the Belgian Science Policy Office, under 464 Grant No. IAP P7- 35 Photonics@be. ANR TOPWAVE, FOPAFE and LABEX CEMPI (ANR-11-LABX-0007) projects, by the French Ministry of Higher Education and Research, the Nord-Pas de Calais Regional Council and Fonds Européen de Développement Régional (FEDER) through the ‘Contrat de Projets Etat Région (CPER)’ and the ‘Campus Intelligence Ambiante (CIA)’. The Einstein Center for Mathematics Berlin under project D-OT2, Collaborative Research Center 123 PlanOS, and Nieders. Vorab Z3061. Spanish MINECO (FIS2015-66503-C3-2-P) and ICREA ACADEMIA. Mardsen Fund of New Zealand. ANR international program, project ANR-2010-INTB-402-02, ‘COLORS’. Italian Ministry of University and Research (MIUR, Project No.2012BFNWZ2). We acknowledge support from the Laboratoire d’Excellence CEMPI (Centre Européen pour les Mathématiques, la Physique et leurs Interactions).

Coupled oscillators can exhibit complex self-organization behavior such as phase turbulence, spatiotemporal intermittency, and chimera states. The latter corresponds to a coexistence of coherent and incoherent states apparently promoted by nonlocal or global coupling. Here we investigate the existence, stability properties, and bifurcation diagram of chimera-type states in a system with local coupling without different time scales. Based on a model of a chain of nonlinear oscillators coupled to adjacent neighbors, we identify the required attributes to observe these states: local coupling and bistability between a stationary and an oscillatory state close to a homoclinic bifurcation. The local coupling prevents the incoherent state from invading the coherent one, allowing concurrently the existence of a family of chimera states, which are organized by a homoclinic snaking bifurcation diagram.

Parametric instability of quasi-reversal system — i.e. time reversible systems perturbed with injection and dissipation of energy — is studied in a unified manner. We infer and characterize an adequate amplitude equation, which is the parametrically driven damped nonlinear Schrödinger equation, corrected with higher order terms. This model exhibits rich dynamical behavior which are lost in the parametrically driven damped nonlinear Schrödinger equation such as: uniform states, fronts and coherent states. The dynamical behavior of a simple parametrically driven system, the vertically driven chain of pendula, exhibits quite good agreement with the amended amplitude equation.

International audience; Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber.This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

We report the theoretical and experimental demonstration of one-dimensional drifting patterns generated by asymmetrical Fourier filtering in the transverse plane of an optical feedback system with a Kerr type nonlinearity. We show, with good agreement between our theoretical (analytics and numerics) calculations and experimental observations that at the primary instability threshold the group velocity is always different from zero. Consequently, the system is convective at this threshold, then exhibits drifting patterns.

A complete description of properties of the wave-train bifurcating from unstable basic oscillatory states (CW nonlinear stationary states) of the nonlinear Schrodinger equation are studied in the moving frames of reference as an initial value problem and using the methods of absolute and convective instabilities. The predictions are in excellent agreement with numerical solutions and may contribute understanding the nonlinear Schrodinger equation complex dynamics under various initial conditions including, localized and/or noisy initial conditions.

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.

International audience; It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schrödinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schrödinger equation. The additional compression points are generated in pairs forming a comblike structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine solitons are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schrödinger equation.

Macroscopic systems with dissipation and time-modulated injection of energy, parametrically driven systems, can self-organize into localized states and/or patterns. We investigate a pulse that travels over a one-dimensional pattern in parametrically driven systems. Based on a minimal prototype model, we show that the pulses emerge through a subcritical Andronov-Hopf bifurcation of the underlying pattern. We describe a simple physical system, a magnetic wire forced with a transverse oscillatory magnetic field, which displays these traveling pulses.

We study secondary instabilities in a coherently driven passive optical fiber cavity. We show that time-modulated solutions which are generated at the onset of instability experience convective and absolute Eckhaus instabilities. The splitting of the secondary instabilities into convective and absolute instabilities drastically impacts the instability boundaries. As a consequence, the stability range of time-modulated waves is enlarged. More importantly, the threshold of absolute instability determines the transition from time-periodic wave trains to a chaotic regime. In the latter the wave trains are composed of irregular oscillations embedded in regular ones. The predictions are in excellent agreement with numerical simulations.

The frequency spectrum asymmetry observed in fiber systems is shown to originate from a nonlinear symmetry breaking. Analytical and experimental results are in excellent agreement. Rogue waves formation in strongly nonlinear regimes is presented.

Macroscopic magnetic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Pattern formation from a uniform magnetization state, induced by the combination of a spin-polarized current and an external magnetic field, is studied for spin-transfer nano-oscillator devices. The system is described in the continuous limit by the Landau-Lifshitz-Gilbert equation. The bifurcation diagram of the quintessence parallel state, as a function of the external field and current, is elucidated. We have shown analytically that this state exhibits a spatial supercritical quintic bifurcation, which generates in two spatial dimensions a family of stationary stripes, squares, and superlattice states. Analytically, we have characterized their respective stabilities and bifurcations, which are controlled by a single dimensionless parameter. This scenario is confirmed numerically.

International audience; We consider a photonic crystal fiber resonator pumped by a coherent injected beam. We show that temporal cavity solitons exhibit a motion with a constant velocity. This regular drift is induced by a broken reflection symmetry mediated by a third-order dispersion. We focus the analysis on dark temporal cavity solitons. They consist of asymmetric moving dips in a uniform background of the intensity profile. The number of the moving dips and their temporal distribution are determined solely by the initial conditions. We characterize this motion by computing the velocity of the dark temporal cavity soliton. Without fourth-order dispersion, dark cavity solitons do not exist.

International audience; Parametrically driven extended systems exhibit dissipative localized states. Analytical solutions of these states are characterized by a uniform phase and a bell-shaped modulus. Recently, a type of dissipative localized state with a nonuniform phase structure has been reported: the phase shielding solitons. Using the parametrically driven and damped nonlinear Schrödinger equation, we investigate the main properties of this kind of solution in one and two dimensions and develop an analytical description for its structure and dynamics. Numerical simulations are consistent with our analytical results, showing good agreement. A numerical exploration conducted in an anisotropic ferromagnetic system in one and two dimensions indicates the presence of phase shielding solitons. The structure of these dissipative solitons is well described also by our analytical results. The presence of corrective higher-order terms is relevant in the description of the observed phase dynamical behavior.

The front dynamics connecting two states of a bistable system is a problem concerning many domains of physics. In an ideally spatial homogeneous potential system, except at the Maxwell point, the front propagates. A spatial periodic forcing has been proposed to lock the drift of the front. In optics, where spatial pumping is usually Gaussian, one can wonder how will turn the dynamics of fronts. We report here front pinning due to the Gaussian optical forcing. The final pattern is a localized state bounded by two pinned fronts. The experimental setup is composed by a Kerr cavity submitted to negative diffraction that allows for the generation of fronts.

Dynamic behaviors of fronts connecting standing waves, such as the locking phenomenon, pinning-depinning transitions, propagation, and front interactions, are studied. Two systems are considered, a vertically driven pendulum chain and a generalized ${\ensuremath{\phi}}^{4}$ model. Both models exhibit in an appropriate region of parameters bistability between standing waves. In the driven pendulum chain, using a Galerkin expansion we characterize the region of bistability between subharmonic waves for the upright and the upside-down pendulum states. We derive analytically the front dynamics in the generalized ${\ensuremath{\phi}}^{4}$ model, showing regions where fronts are oscillatory or propagative. We also characterize the mechanism of the pinning-depinning transition of fronts between standing waves. Using front interactions we predict the emergence of dissipative localized waves supported on a standing wave and characterize their corresponding homoclinic snaking bifurcation diagrams. All these analytical predictions are confirmed by numerical simulations with quite good agreement.