Related papers: Traveling waves for a lattice dynamical system ari…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We study the weak interaction between a pair of well-separated coherent structures in possibly non-local lattice differential equations. In particular we prove that if a lattice differential equation in one space dimension has…
The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features,…
The interaction between waves and evolving media challenges traditional conservation laws. We experimentally investigate the behavior of elastic wave packets crossing a moving interface that separates two media with distinct propagation…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…
Wave transport devices, such as amplifiers, frequency converters, and nonreciprocal devices, are essential for modern communication, signal processing, and sensing applications. Of particular interest are traveling wave setups, which offer…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics. The presented framework is based on the steadily-propagating traveling wave ansatz, $u(x,t) = U(\xi=x…
Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size.…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave…
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves…
In this work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic…
The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj in[1], but are applicable to vector…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…