Extreme wave excitation from localized phase-shift perturbations.

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of sidebands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this Letter, we show that phase-shift localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers, and thus by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such a focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.

Nonlinear wave evolution with data-driven breaking.

Wave breaking is the main mechanism that dissipates energy input into ocean waves by wind and transferred across the spectrum by nonlinearity. It determines the properties of a sea state and plays a crucial role in ocean-atmosphere interaction, ocean pollution, and rogue waves. Owing to its turbulent nature, wave breaking remains too computationally demanding to solve using direct numerical simulations except in simple, short-duration circumstances. To overcome this challenge, we present a blended machine learning framework in which a physics-based nonlinear evolution model for deep-water, non-breaking waves and a recurrent neural network are combined to predict the evolution of breaking waves. We use wave tank measurements rather than simulations to provide training data and use a long short-term memory neural network to apply a finite-domain correction to the evolution model. Our blended machine learning framework gives excellent predictions of breaking and its effects on wave evolution, including for external data.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Nonconservative higher-order hydrodynamic modulation instability.

The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.

Experimental Observation and Theoretical Description of Multisoliton Fission in Shallow Water.

We observe the dispersive breaking of cosine-type long waves [Phys. Rev. Lett. 15, 240 (1965)] in shallow water, characterizing the highly nonlinear "multisoliton" fission over variable conditions. We provide new insight into the interpretation of the results by analyzing the data in terms of the periodic inverse scattering transform for the Korteweg-de Vries equation. In a wide range of dispersion and nonlinearity, the data compare favorably with our analytical estimate, based on a rigorous WKB approach, of the number of emerging solitons. We are also able to observe experimentally the universal Fermi-Pasta-Ulam recurrence in the regime of moderately weak dispersion.

Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence.

Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. One prominent form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI leads to a growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrödinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios.

Hydrodynamics of periodic breathers.

We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov-Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.

Gray solitons on the surface of water.

The dynamics of surface gravity water waves can be described by the self-defocusing nonlinear Schrödinger equation. Recent observations of black solitons on the surface of water confirmed its validity for finite, below critical depth. The black soliton is a limiting case of a family of gray soliton solutions with finite amplitude depressions. Here, we report observations of gray solitons in water waves, thus, complementing our previous observations of black solitons.

Hydrodynamic supercontinuum.

We report the experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves. Higher-order N-soliton solutions with N=2, 3 are studied in detail and shown to be associated with self-focusing in the wave group dynamics and the generation of a steep localized carrier wave underneath the group envelope. We also show that for larger input soliton numbers, the wave group experiences irreversible spectral broadening, which we refer to as a hydrodynamic supercontinuum by analogy with optics. This process is shown to be associated with the fission of the initial multisoliton into individual fundamental solitons due to higher-order nonlinear perturbations to the NLS. Numerical simulations using an extended NLS model described by the modified nonlinear Schrödinger equation, show excellent agreement with experiment and highlight the universal role that higher-order nonlinear perturbations to the NLS play in supercontinuum generation.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Experimental observation of dark solitons on the surface of water.

We present the first ever observation of dark solitons on the surface of water. It takes the form of an amplitude drop of the carrier wave which does not change shape in propagation. The shape and width of the soliton depend on the water depth, carrier frequency, and the amplitude of the background wave. The experimental data taken in a water tank show an excellent agreement with the theory. These results may improve our understanding of the nonlinear dynamics of water waves at finite depths.

Observation of a hierarchy of up to fifth-order rogue waves in a water tank.

We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrödinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.

Experimental study of spatiotemporally localized surface gravity water waves.

We present experimental results on the study of spatiotemporally localized surface wave events on deep water that can be modeled using the Peregrine breather solution of the nonlinear Schrödinger equation. These are often considered as prototypes of oceanic rogue waves that can focus wave energy into a single wave packet. For small steepness values of the carrier gravity waves the Peregrine breathers are relatively wide, thus providing an excellent agreement between the theory and experimental results. For larger steepnesses the focusing leads to temporally and spatially shorter events. Nevertheless, agreement between measurements and the Peregrine breather theory remains reasonably good, with discrepancies of modulation gradients and spatiotemporal symmetries being tolerable. Lifetimes and travel distances of the spatiotemporally localized wave events determined from the experiment are in good agreement with the theory.

Rogue wave observation in a water wave tank.

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.

[Lyme borreliosis situation in North Africa]. / Situation de la borreliose de Lyme au Maghreb.

Many epidemiological studies were conducted for studying Lyme borreliosis (LB) which represents a new global public health problem. It is now the most common vector-borne disease in Europe and North America. The causative agent Borrelia burgdorferi sl is a bacterial species complex comprising 12 delineated and named species. In North Africa, few studies based on clinical and serological features, have suggested that LB could occur. Indeed, recent studies conducted in Tunisia, Algeria and Morocco have showm that Ixodes ricinus is present in cooler and humid area of these regions. These studies also revealed that this species is a vector of B. burgdorferi sl with high prevalence of infection. Using IFI and PCR tests, the mean rate of Borrelia-infection ranged from 50 to 60% in I. ricinus adult collected in Tunisia and Morocco and from 30 to 40% in nymphs; in contrast, the prevalence in larvae is less than 2.5%. Several strains of B. burgdorfer were isolated from adult and nymph I ricinus collected in Tunisia and Morocco. The identification of these strains and DNAs directly extracted from Ixodes was done by PCR-RFLP and sequence analysis. The results showed that B. lusitaniae (genotypes Poti B2 and Poti B3) is the predominant species circulating in I. ricinus in Tunisia and Morocco, B. garinii and B. burgdorferi ss and B lusitaniae were also present but very rare. These results provide the evidence for the existence of B. burgdorferi sl in North Africa; however, the impact of LB in the human population seem to be negligible and the seroprevalence of Borrelia in forest workers (considered as population at high risk) in Tunisia is less than 4%.

[Diagnosis of holoprosencephalia. Report of 17 cases]. / Diagnostic de l'holoprosencephalie. A propos de 17 cas.

OBJECTIVE: To establish the epidemiologic profile of holoprosencephalia and determine benefits of ultrasound and foetopathologic examination to the diagnostic. METHODS AN MATERIAL: [corrected] Retrospective study about 17 cases of holoprosencephalia observed in CMNT between Janaury 1992 and September 2000. RESULTS: Ultrasound diagnosis was made in 13 cases (75%). Ultrasound criteria were; absence of median structure of the brain and unique ventricule. The prognosis was always bad. Foetopathologic examination revealed 7 cases of lobar holoproencephalia and 10 of semi lobar. Fascial dysmorphia were noted in 82% of cases. CONCLUSION: The foetopathology and genetic counselling looking for fascial, dysmorphia in family's members gives a good evaluation of recurrences.

[Incidence and seroprevalence of canine ehrlichiosis in the Medjez El Bab region (northwestern Tunisia during 1994, 1995 and 1996]. / Incidence et séroprévalence de l'ehrlichiose canine dans la région de Medjez El Bab (nord-ouest de la Tunisie) pendant les années 1994, 1995 et 1996.

A sero-epidemiological survey, realized in the Medjez El Bab region (North-West of Tunisia), has concerned 180 dogs which status has been determined during the study. The animals were identified, then underwent an annual blood sampling during three successive years, in order to search for antibodies against E. canis and E. chaffeensis by indirect immunofluorescence. The results show that, in all sero-positive dogs, the levels of antibodies against E. canis were higher than those against E. chaffeensis. The sero-prevalence of E. canis was 42.8%, 50% and 48.9%, in 1994, 1995 and 1996, respectively, and was higher than that against E. chaffeensis during the three year studies. The incidence of E. canis infection was 12.6% during the three years whereas E. chaffeensis infection did not exceed 4.7%.

[Epizootic equine influenza in Tunisia]. / A propos d'une épizootie de grippe équine survenue en Tunisie.

The authors describe an equine influenza epizootic that occurred in Tunisia during February and March 1998 in the regions of Tozeur, Sousse and Tunis. They relate the symptoms, the different stages of diagnosis and the serological results.

[Tracheal atresia. A case report]. / Atresie tracheale. A propos d'un cas.

The tracheal agenesis is a rare malformation of the respiratory tract. It must be suspected in any new born with respiratory distress, absence of crying, and difficulty or impossibility of intubation. Since the initial case report by Payne in 1900, 87 cases have been reported in the literature. The authors report one case of tracheal agenesis out of 2500 autopsy realised in the laboratory.