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Dissipationless hydrodynamics regularized by dispersion describe a number of physical media including water waves, nonlinear optics, and Bose-Einstein condensates. As in the classical theory of hyperbolic equations where a non-convex flux…
Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in…
Compressional waves propagating in the partially ionised solar lower atmospheric plasmas can easily steepen into nonlinear waves, including shocks. Here we investigate the effect of weak dispersion generated by Hall currents perpendicular…
We develop a self-consistent method to study the optical response of metallic gratings with nonlinear media embedded within their subwavelength slits. An optical Kerr nonlinearity is considered. Due to the large E-fields associated with the…
Nonlinear plane acoustic waves propagating through a fluid are studied using Burgers' equation with finite viscosity. The evolution of a simple N-pulse with regular and random initial amplitude and of pulses with monochromatic and noise…
This note analytically investigates non-reciprocal wave dispersion in locally resonant acoustic metamaterials. Dispersion relations associated with space-time varying modulations of inertial and stiffness parameters of the base material and…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be…
We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such system is governed by a higher-order nonlinear Schr%…
Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are…
Shock waves are examples of the far-from-equilibrium behaviour of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive…
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a…
We examine the propagation of electromagnetic radiation through a strong magnetic field using the method of characteristics. Owing to nonlinear effects associated with vacuum polarization, such waves can develop discontinuities analogous to…
Ocean rogue waves (RW) -huge solitary waves- have for long triggered the interest of scientists. RWs emerge in a complex environment and it is still dubious the importance of linear versus nonlinear processes. Recent works have demonstrated…
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…
A theoretical study of wave propagation in 1D metamaterial is presented. A system of nonlinear evolution equation for electromagnetic waves with both polarizations account is derived by means of projection operators method for general…
All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states…
We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system.…
Linear stability analysis of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity) is performed. The speckle…
Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to…