Related papers: Nonlinear self-adapting wave patterns
The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small lengthscales. Here, wave turbulence is observed in experiments on a vibrating plate. The…
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable…
We study traveling waves for reaction diffusion equations on the spatially discrete domain $\Z^2$. The phenomenon of crystallographic pinning occurs when traveling waves become pinned in certain directions despite moving with non-zero wave…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow…
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…
The modulational instability of waves in a medium under the action of an external monochromatic force and dissipation is considered. The model which describes the nonlinear stage of the modulation instability was constructed with using…
We study a population of swarmalators (swarming/mobile oscillators) which run on a ring and are subject to random pinning. The pinning represents the tendency of particles to stick to defects in the underlying medium which competes with the…
We derive and justify analytically the dynamics of a small macroscopically modulated amplitude of a single plane wave in a nonlinear diatomic chain with stabilizing on-site potentials including the case where a wave generates another wave…
Nonequilibrium dynamics of biomembranes with active inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with ATP ligands. As protein…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at…
We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…
This work presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the longitudinal axis of the filter. The model is formulated as a system of partial differential…
Quantum mechanics predicts that massive particles exhibit wave-like behavior. Matterwave interferometry has been able to validate such predictions through ground-breaking experiments involving microscopic systems like atoms and molecules.…
The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced…
In this paper, we present a complete classification of traveling wave solutions for monostable systems within a unified framework. To this end, we introduce a novel technique, referred to as the slicing method, which is based on the…