We study a cooperative system of integro-differential equations. It is shown that the system in general has multiple spreading speeds, and when the linear determinacy conditions are satisfied all the spreading speeds are the same and equal to the spreading speed of the linearized system. The existence of traveling wave solutions is established via integral systems. It is shown that when the lin...

Electroabsorption modulators (EAMs) based on the quantum confined Stark effect in multiple quantum wells (MQWs) have advantages for high-speed, low drive voltage, and high extinction ratio applications. In this paper, a traveling-wave electrode structure is proposed to achieve high bandwidths with long devices and lower drive voltages at 1.55μm wavelength. An InGaAsP/InGaAsP MQW traveling-wave ...

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the sprea...

In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay ∂u (x, t) ∂t = d u (x, t)+ f ⎛ ⎝u (x, t) , ∞ ∫ −∞ h (x − y) u (y, t − τ) dy ⎞ ⎠. Under the monostable assumption, we show that there exists a minimal wave speed c∗ > 0, such that the equation has no traveling wave front for 0 < c < c∗ and a tr...

This paper is concerned with the following two-species LotkaVolterra competition-diffusion system in the three-dimensional spatial space { ∂ ∂t u1(x, t) = ∆u1(x, t) + u1(x, t) [1− u1(x, t)− k1u2(x, t)] , ∂ ∂t u2(x, t) = d∆u2(x, t) + ru2(x, t) [1− u2(x, t)− k2u1(x, t)] , where x ∈ R3 and t > 0. For the bistable case, namely k1, k2 > 1, it is well known that the system admits a one-dimensional mo...

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the constructi...

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.

The emergence of very stable traveling intrinsic localized modes (ILMs) locked to a uniform driver is demonstrated in a discrete electrical transmission line. The speed of these traveling ILMs is tunable by the driver amplitude and frequency. It is found to be quite sensitive to the ratio of intersite to on-site nonlinearity. The number of traveling ILMs can also be selected via the driving con...

We study the existence of traveling waves in a one-dimensional network of integrateand-fire neurons with finite support coupling. We show that when the reset after spiking is sufficiently low, the interspike intervals (ISIs) for a traveling wave with an explicit first wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion re...