Non
Linear
Physics
Group -
Eric Falcon
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160 years after the first observation of a solitary wave hump (positive) on the surface of water and modelled by Korteweg and De Vries (KdV) equation, we observed experimentally for the first time a KdV solitary wave of depression type (negative). It was nevertheless known since 1895 that dispersion could change sign, and thus the shape of the wave (positive or negative) if the effect of the surface tension is important. These results were widely commented in the scientific press. [see PRL2002]
Solitary waves are ubiquitous nonlinear structures that appear in a wide range of physical systems. However, fifth-order dispersive Korteweg-de Vries (KdV) solitary waves, theoretically predicted in the 1970s, have so far eluded experimental observation, although they are expected to be found in hydrodynamics, plasmas, hydroelastic media, and electrical grids.
We reported the first experimental observation of these solitary waves in a tunable nonlinear electrical transmission line. By introducing mutual inductive coupling between neighboring lattice elements, we remove cubic dispersion, thus gaining access to a regime where fifth-order dispersion dominates. Direct spatiotemporal measurements then reveal this dispersive behaviour sought. To our knowledge, this work presents the first controlled experimental characterization of fifth-order KdV solitary waves (KdV5) [see Fache, sumitted2026]. The measured profiles, the amplitude-width and amplitude-velocity relationships, and the dynamics of the collisions (including frontal and overtaking collisions) are quantitatively consistent with theoretical predictions. This breakthrough not only validates a long-established theoretical model, but also paves the way for the observation of these solitary waves in other physical systems, including internal waves, magnetized plasmas, and ice-covered oceans, where their detection remains a challenge.
Solitons occur in various fields of physics, but their propagation in a periodic or random medium remains unexplored experimentally. We have highlighted different dynamics of a soliton on the surface of a fluid in a 4-m-long canal with a flat, periodic, or disordered bottom. Fission into multiple solitons is reported for the periodic bottom, whereas scattering into dispersive waves is observed for the disordered topography. We also answer the long-standing debate about how a soliton is impacted by disorder in the context of Anderson localization and how localization depends on nonlinearity. First discovered in solid-state physics in the 1950s, Anderson localization leads to linear waves remaining trapped, or localized, within a random medium. Although this phenomenon occurs in almost all areas of wave physics in random media, its persistence for nonlinear pulses or solitons had not been experimentally resolved until this study using hydrodynamics waves. This study paves the way for potential coastal protection against large-amplitude waves such as tsunamis, by influencing the bathymetry of the seabed. [see PRL2024]. 
We have achieved to generate an inverse cascade regime of surface-gravity wave turbulence in a large-scale basin (50 m x 30 m and 5 m) [see PRL2020]. Such wave fields are valuable for the study of rogue waves since the random waves involved in their dynamics are generated by the nonlinear wave interactions rather than directly forced by a wave maker. We have then reported statistics of thousands of rogue waves in a large-scale basin and demonstrated that some of their properties crucially depend on four-wave resonant interactions (large crests being for instance more likely than predicted by second-order models) [see JFM2022]. 
We have performed several campaigns within a 150 m long wave channel at ECN, Nantes, France, to experimentally test various aspects related to integrable turbulence, i.e., non-equilibrium, stationary theoretical states arising from the dynamics of a random initial condition within an integrable equation. We have obtained the first controlled synthesis of a dense gas of solitons in deep-water random surface gravity waves, using the tools of nonlinear spectral theory (inverse scattering transform - IST) for the one-dimensional focusing nonlinear Schrödinger equation (NLS). The soliton gas is experimentally generated in a 150-m long water tank instrumented with twenty wave elevation gauges. The obtained results represent the first crucial step for the experimental validation of the kinetic theory of soliton gases, and pave the way for further studies in nonlinear optics, superfluid or oceanography [see PRL2020b]. We then obtained, for the first time experimentally, the interaction between two soliton gases (synthesized by the IST), which is in good agreement with the spectral kinetic theory of soliton gases [see PRE2024 (PRE Editors' Suggestion)]. 
By means of an original technique, we achieved experimentally to form a stable torus of liquid and to report the resonance frequencies of a torus of liquid [see PRL2019]. By improving the technique, we have reported the full dispersion relation of azimuthal waves along a torus of fluid [see PRL2021]. We have also reported the observation of nonlinear three-wave resonant interactions between two different branches of the dispersion relation, namely the gravity-capillary and sloshing modes [see PRE2023]. 
One feature of the propagation of linear waves in dispersive medium is the existence of precursors (or forerunners). This terminology traces back to the fact that they generally arrive earlier than the main signal. This transient response is due to the propagation of the fastest high frequency components of the spectrum of the initial excitation. Although predicted since 1914 by Sommerfeld and Brillouin, the experimental observations remain rare and qualitative, and relate to mainly the electromagnetic waves in a dielectric medium.
