Related papers: Self-sustained nonlinear waves in traffic flow
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
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…
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state…
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…
We study a model for freeway traffic which includes strong noise taking into account the fluctuations of individual driving behavior. The model shows emergent traffic jams with a self-similar appearance near the throughput maximum of the…
Merging junctions are important network bottlenecks, and a better understanding of merging traffic dynamics has both theoretical and practical implications. In this paper, we present continuous kinematic wave models of merging traffic flow…
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
It is well known that long Josephson tunnel junctions (JTJs) act as active transmission lines for the slow-mode propagation of magnetic flux-quanta (in the form of solitary waves) that is at the base of many superconducting circuits. At the…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
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…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…
A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed…
In this paper, we concerned with the propagation of sound waves through stratified media. Transport equation of nonlinear geometric optics in media with mixed nonlinearity, in the case of spatially varying density and entropy fields, is…
A quantum particle transport induced in a spatially-periodic potential by a propagating plane wave has a number important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices…
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…