Related papers: Compact Waves in Microscopic Nonlinear Diffusion
We study the diffusion-limited reaction A + A <-> A in different spatial dimensions to observe the effect of internal fluctuations on the interface between stable and unstable phases. We find that, similar to what has been observed in d=1…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion…
We study the k-space fluctuations of the waveaction about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the Random Phase Approximation (RPA) and derive evolution equations for the arbitrary-order…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
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…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence $D(x)\sim|x|^{\alpha}$ of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on…
In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the…
A fourth-order and a second-order nonlinear diffusion models in spectral space are proposed to describe gravitational wave turbulence in the approximation of strongly local interactions. We show analytically that the model equations satisfy…
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized (Anderson localization). The width of the eigenvalue spectrum, and the average eigenvalue spacing inside the localization volume, set two…
We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce…
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…
We consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere---a regime characterized by small large-scale Rossby…
We study a 2D lattice model of forward-directed waves in which the integrated intensity for classical waves (or probability for quantum mechanical particles) is conserved. The model describes the time evolution of 1D quantum particle in a…