Related papers: Exact expression for the propagating front velocit…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation…
We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
Ocean wind waves are a fundamental manifestation of complex dynamics in geophysical fluid systems, characterized by a rich interplay between dispersion and nonlinearity. While linear wave theory provides a first-order description of wave…
Density-wave fronts in a vibrofluidized wet granular layer undergoing a gas-liquid-like transition are investigated experimentally. The threshold of the instability is governed by the amplitude of the vertical vibrations. Fronts, which are…
The theory of internal waves between two layers of immiscible fluids is important both for its applications in oceanography and engineering, and as a source of interesting mathematical model equations that exhibit nonlinearity and…
Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from…
We show that the self-interactions present in the effective field theory formulation of general relativity can couple gravitational wave modes and generate nonclassical states. The output of gravitational nonlinear processes can also be…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of…