Pattern Formation and Solitons
Attenuation of short, strongly nonlinear stress pulses in chains of spheres and cylinders was investigated experimentally and numerically for two ratios of their masses keeping their contacts identical. The chain with mass ratio 0.98…
We report optical fiber experiments allowing to investigate integrable turbulence in the focusing regime of the one dimensional nonlinear Schr\"odinger equation (1D-NLSE). Our experiments are very similar in their principle to water tank…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi--Pasta--Ulam (FPU) lattices. The growth of the instability is followed by a process of relaxation to…
Three-dimensional excitable systems can selforganize vortex patterns that rotate around one-dimensional phase singularities called filaments. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations, we pin these…
We introduce a ladder-shaped chain with each rung carrying a $\mathcal{PT}$ -symmetric gain-loss dipole. The polarity of the dipoles is staggered along the chain, meaning that a rung bearing gain-loss is followed by one bearing loss-gain.…
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid.…
We investigate a regenerative memory based upon a time-delayed neuromorphic photonic oscillator and discuss the link with temporal localized structures. Our experimental implementation is based upon a optoelectronic system composed of a…
In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each of which the non-linear wave equation is homogeneous. In such…
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} ({\bPsi} \Psi)^{\kappa+1}$ in the presence of various external electromagnetic fields. Starting from the exact…
A direct numerical simulation of Faraday waves is carried out in a minimal hexagonal domain. Over long times, we observe the alternation of patterns we call quasi-hexagons and beaded stripes. The symmetries and spatial Fourier spectra of…
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…
Three-dimensional excitable systems can create nonlinear scroll waves that rotate around one-dimensional phase singularities. Recent theoretical work predicts that these filaments drift along step-like height variations. Here we test this…
Beams made from thin-walled elements, whilst very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on…
Slime mould Physarum polycephalum builds up sophisticated networks to transport nutrients between distant part of its extended body. The slime mould's protoplasmic network is optimised for maximum coverage of nutrients yet minimum energy…
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the…
Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…
We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a…
We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas". As…
In the present work we focus on the case of (few-site) configurations respecting the PT-symmetry. We examine the case of such "oligomers" with not only 2-sites, as in earlier works, but also the cases of 3- and 4-sites. While in the former…