Inside Dynamics of Delayed Traveling Waves

Deformation of Traveling Waves in Delayed Cellular Neural Networks

In this paper, we establish the existence and describe the global structure of traveling waves for a class of lattice delay differential equations describing cellular neural networks with distributed delayed signal transmission. We describe the transition of wave profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. We a...

Nonlinear dynamics of short traveling capillary-gravity waves.

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the special case theta=1/3 is not studied). These waves become singular when their amplitude is larger than...

Structure and Dynamics of Modulated Traveling Waves in Cellular Flames

We describe the formation and evolution of spatial and temporal patterns in cylindrical premixed flames. We consider the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if Le is decreased bel...

Traveling Waves in a Simplified Model of Calcium Dynamics

Traveling Waves and Power Waves

M icrowave equivalent-circuit theory is like a grand old building: elegant, carefully crafted, passed from generation to generation, and rooted in history. Traveling waves, the measureable electromagnetic field solutions of Maxwell’s equations in a transmission line, form the foundation of the theory. You must descend into the basement to see them; not many people do so. It is in this “basement...