相关论文: Multichromatic travelling waves for lattice Nagumo…

We study the optical response of a 2D square lattice of atoms using classical electrodynamics. Due to dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with…

Selective optical excitation of a substrate lattice can drive phase changes across hetero-interfaces. This phenomenon is a non-equilibrium analogue of static strain control in heterostructures and may lead to new applications in optically…

We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…

We study the Mackey-Glass type monostable delayed reaction-diffusion equation with a unimodal birth function $g(u)$. This model, designed to describe evolution of single species populations, is considered here in the presence of the weak…

We construct entire solutions of bistable reaction-diffusion equations by mixing finite planar fronts, which form a finite-dimensional manifold. These entire solutions are generalized traveling fronts, that is, transition fronts. We also…

Antichiral surface states, characterized by unidirectional propagation on parallel surfaces, offer unique potential for controlling classical waves. However, their realization typically relies on complex implementations of the…

Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…

Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key role in mathematical biology and in particular in the study of…

The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and…

We investigate the vacuum realignment for chiral symmetry breaking and color superconductivity at finite density in Nambu-Jona-Lasinio model in a variational method. The treatment allows us to investigate simultaneous formation of…

We show that double-charge discrete optical vortices may be completely stable in hexagonal photonic lattices where single-charge vortices always exhibit dynamical instabilities. Even when unstable the double-charge vortices typically have a…

In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular,…

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…

When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a…

We present a magnetoelastic lattice in which a localized external magnetic field, generated by an assembly of fixed magnets, tunes the potential landscape to create monostable, bistable, and tristable configurations. Focusing on the…

A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These are proven to exhibit a dynamical glass transition: above a critical density, rho_c, ergodicity is broken due to the appearance of an…

This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…

We investigate the stability of traveling-pulse solutions to the stochastic FitzHughNagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling…