arXiv subjects

François Copie

Publications and source records attributed to François Copie.

14 recordsLinked to original sources

arXiv2026

Exact Charge, Current, and Velocity Fields of Interacting Korteweg-de Vries Solitons

Solitons in integrable systems exhibit a dual wave-particle character, yet their identification as individual objects becomes ambiguous during interactions, where they deform and delocalize. We develop a microscopic, field-based description that resolves this issue by introducing exact space-time fields of charge, current, and velocity derived from the inverse scattering transform (IST) of the Korteweg-de Vries (KdV) equation. This framework enables individual KdV solitons to be tracked throughout interactions, providing a quantitative description of their trajectories and deformation beyond the asymptotic regime. We show that the dynamics of $N$ interacting solitons can be formulated in terms of $N$ independent continuity equations, in which interactions are encoded in initial correlations that are subsequently propagated. From this microscopic viewpoint, effective velocities and hydrodynamic behavior emerge upon coarse graining, recovering kinetic theory of soliton gases and Generalized Hydrodynamics as scaling limits. Our results establish a direct connection between the wave-based IST formalism and particle-like emergent descriptions, offering a unified framework for soliton dynamics across scales.

nlin.PS↗

arXiv2026

Diffraction of deep-water solitons

Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional systems, but introducing additional spatial dimensions is generally expected to destabilize them or destroy their coherent character. Here we experimentally investigate how deep-water gravity-wave solitons behave when a controlled transverse degree of freedom is introduced through diffraction. Using a large-scale water-wave facility, we generate solitonic wave packets whose transverse structure is imposed across a segmented wavemaker through either a sharp slit or a smooth Gaussian apodization. The resulting two-dimensional wave fields are measured with high spatial resolution. Diffraction reshapes the transverse profile of the wave packet while its longitudinal dynamics retain the characteristic features of a soliton. Nonlinear spectral analysis confirms that the solitonic content is preserved along the direction of propagation, whereas the transverse evolution follows the linear Fresnel laws of diffraction. These observations reveal an unexpected coexistence of nonlinear soliton dynamics and classical wave diffraction.

nlin.PS↗

arXiv2025

Controlled manipulation of solitons in a recirculating fiber loop using external potentials

Optical solitons are self-sustained wave packets that propagate without distortion due to a balance between dispersion and nonlinearity. Their unique stability underpins key photonic applications while also playing a central role in nonlinear wave physics. However, real-time control over soliton dynamics in non-dissipative systems remains a major challenge, limiting their practical applications in photonic systems. Here, we introduce a fiber-based platform for soliton manipulation, by creating programmable external potentials through synchronous arbitrary phase modulation in a recirculating optical fiber loop. We demonstrate precise soliton trapping, parametric excitation, and coupled multi-soliton interactions, revealing particle-like behavior in excellent agreement with a Hamiltonian description in which solitons are treated as interacting classical particles. The strong analogy with matter-wave solitons in Bose-Einstein condensates highlights the broader implications of our approach, which provides a versatile experimental tool for the study of nonlinear wave dynamics and engineered soliton manipulation.

nlin.PS↗

arXiv2025

The effect of discrete-time evolution on thermalisation in a lattice

Particles subject to weak contact interactions in a finite-size lattice tend to thermalise. The Hamiltonian evolution ensures energy conservation and the final temperature is fully determined by the initial conditions. In this work we show that equilibration processes are radically different in lattices subject to discrete-step unitary evolution, which have been implemented in photonic circuits, coin polarisation walkers and time-multiplexed pulses in fibres. Using numerical simulations, we show that weak nonlinearities lead to an equilibrium state of equal modal occupation across all the bands, i.e, a thermal state with infinite temperature and chemical potential. This state is reached no matter the initial distribution of modes and independent of the bands dispersions and gaps. We show that by engineering the temporal periodicity inherent to these systems, equilibration can be accelerated through resonant Floquet channels. Our results demonstrate that discrete time plays a crucial role in wave dynamics, fundamentally altering thermalisation processes within weak wave turbulence theory.

physics.optics↗

arXiv2025

Experimental observation of the spatio-temporal dynamics of breather gases in a recirculating fiber loop

We report the first experimental observation of breather gases (BGs) in optics, realized in a recirculating fiber loop enabling virtually lossless propagation over $1200$ km. Initiated by a slowly modulated optical background perturbed by noise, the BGs form through a nonlinear fission process and demonstrate spatiotemporal dynamics that align closely with numerical simulations of the focusing one-dimensional nonlinear Schrödinger equation. The minimal dissipation in our setup enables a statistical characterization of the BGs and confirms the theoretically predicted doubling of kurtosis during the evolution of the BGs. These results open new avenues for experimental studies of integrable turbulence involving solitons on finite background.

nlin.PS↗

arXiv2024

Manipulation of strongly interacting solitons in optical fiber experiments

The model underlying physics of guiding light in single-mode fibers -- the one-dimensional nonlinear Schrödinger equation (NLSE), reveals a remarkable balance of the fiber dispersion and nonlinearity, leading to the existence of optical solitons. With the Inverse Scattering Transform (IST) method and its perturbation theory extension one can go beyond single-soliton physics and investigate nonlinear dynamics of complex optical pulses driven by soliton interactions. Here, advancing the IST perturbation theory approach, we introduce the eigenvalue response functions, which provide an intuitively clear way to manipulate individual characteristics of solitons even in the case of their entire overlapping, i.e. very strong interactions. The response functions reveal the spatial sensitivity of the multi-soliton pulse concerning its instantaneous perturbations, allowing one to manipulate the velocities and amplitudes of each soliton. Our experimental setup, based on a recirculating optical fiber loop system and homodyne measurement, enables observation of long-distance NLSE dynamics and complete characterization of optical pulses containing several solitons. Adding a localized phase perturbation on a box-shaped wavefield, we change individual soliton characteristics and can detach solitons selectively from the whole pulse. The detached solitons exhibit velocities very close to the theoretical predictions, thereby demonstrating the efficiency and robustness of the response functions approach.

nlin.PS↗

arXiv2024

Dissipation-driven emergence of a soliton condensate in a nonlinear electrical transmission line

We present an experimental study on the perturbed evolution of Korteweg-deVries soliton gases in a weakly dissipative nonlinear electrical transmission line. The system's dynamics reveal that an initially dense, fully randomized, soliton gas evolves into a coherent macroscopic state identified as a soliton condensate through nonlinear spectral analysis. The emergence of the soliton condensate is driven by the spatial rearrangement of the systems's eigenmodes and by the proliferation of new solitonic states due to nonadiabatic effects, a phenomenon not accounted for by the existing hydrodynamic theories.

nlin.PS↗

arXiv2023

Interaction of soliton gases in deep-water surface gravity waves

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. We report hydrodynamic experiments in which we investigate the interaction between two "beams" or "jets" of soliton gases having nearly identical amplitudes but opposite velocities of the same magnitude. The space-time evolution of the two interacting soliton gas jets is recorded in a 140-m long water tank where the dynamics is described at leading order by the focusing one-dimensional nonlinear Schrodinger equation. Varying the relative initial velocity of the two species of soliton gas, we change their interaction strength and we measure the macroscopic soliton gas density and velocity changes due to the interaction. Our experimental results are found to be in good quantitative agreement with predictions of the spectral kinetic theory of soliton gas despite the presence of perturbative higher-order effects that break the integrability of the wave dynamics.

nlin.PS↗

arXiv2023

Space-time observation of the dynamics of soliton collisions in a recirculating optical fiber loop

We present experiments performed in a recirculating fiber loop in which we realize the single-shot observation of the space and time interaction of two and three bright solitons. The space-time evolutions observed in experiments provide clear evidence of a nearly-integrable nonlinear wave dynamics that can be easily interpreted within the framework of the inverse scattering transform (IST) method. In particular collisions between solitons are found to be almost perfectly elastic in the sense that they occur without velocity change and with only a position (time) shift quantitatively well described by numerical simulations of the integrable nonlinear Schrödinger equation. Additionally our experiments provide the evidence that the position (time) shifts arising from the interaction among three solitons are determined by elementary pairwise interactions, as it is well known in the IST theory.

nlin.PS↗

arXiv2022

Spatio-temporal observation of higher-order modulation instability in a recirculating fiber loop

We experimentaly investigate higher-order seeded modulation instability in an optical fiber experiment. The recirculating loop configuration with round-trip losses compensation enables the observation in single-shot of the spatio-temporal evolution of an initially modulated continuous field revealing intricate yet deterministic dynamics. By tuning the modulation period, a continuous transition between perfectly coherent and purely noise-driven dynamics is observed that we characterise by means of a statistical study.

physics.optics↗

arXiv2021

Single shot measurement of the photonic band structure in a Floquet-Bloch lattice realised with coupled fiber rings

Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics. While this type of lattices is difficult to implement in solid-state physics, optical systems have provided excellent platforms to probe their physics: among other effects, they have revealed genuine phenomena such as the anomalous Floquet topological insulator and the funnelling of light into localised interface modes. Despite the crucial importance of the band dispersion in the photon dynamics and the topological properties of the lattice, the direct experimental measurement of the Floquet-Bloch bands has remained elusive. Here we report the direct measurement of the Floquet-Bloch bands of a photonic lattice with a single shot method. We use a system of two coupled fibre rings that implements a time-multiplexed Floquet-Bloch lattice. By Fourier transforming the impulse response of the lattice we obtain the band structure together with an accurate characterization of the lattice eigenmodes, i. e. the amplitudes and the phases of the Floquet-Bloch eigenvectors over the entire Brillouin zone. Our results open promising perspectives for the observation of topological effects in the linear and nonlinear regime in Floquet systems.

physics.optics↗

arXiv2021

Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

We numerically realize breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N $\sim$ 50 breathers via the Darboux transform recursive scheme in high precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma and Peregrine breathers as elementary quasi-particles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial" generic breather (Tajiri-Watanabe) and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory (El and Tovbis, PRE 2020).

nlin.PS↗

arXiv2020

Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. Despite significant theoretical developments and observational evidence of ubiquity of soliton gases in fluids and optical media their controlled experimental realization has been missing. We report the first controlled synthesis of a dense soliton gas in deep-water surface gravity waves using the tools of nonlinear spectral theory (inverse scattering transform (IST)) for the one-dional focusing nonlinear Schrödinger equation. The soliton gas is experimentally generated in a one-dimensional water tank where we demonstrate that we can control and measure the density of states, i. e. the probability density function parametrizing the soliton gas in the IST spectral phase space. Nonlinear spectral analysis of the generated hydrodynamic soliton gas reveals that the density of states slowly changes under the influence of perturbative higher-order effects that break the integrability of the wave dynamics.

nlin.PS↗

arXiv2020

From modulational instability to focusing dam breaks in water waves

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wavepacket towards the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semi-classical limit of the 1D focusing nonlinear Schrodinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semi-classical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

nlin.PS↗