用行波速率方程组确定半导体激光器的输出场

为了解决在平均场近似速率方程中自洽地由激光器腔内平均场来确定输出场的问题,以半导体激光器为例,采用集总形式的端面反射率,通过求解行波速率方程组,得出了半导体激光器腔内平均光子数密度与输出光子数密度的解析关系式.结果表明,半导体激光器输出场与腔内平均场之比是一个与泵浦电流有关的量,把它当成常数是有偏见的.     

Heterogeneity selected target waves and their competition: Outgoing or ingoing?

Traveling direction (outgoing or ingoing) of target waves sustained by a localized inhomogeneity and their competition rules in the complex Ginzburg-Landau equation (CGLE) are studied. We show that even a local positive (negative) frequency shift is capable of creating ingoing (outgoing) target waves. A novel transition between ingoing and outgoing target waves, as we find, can be switched by the size of the inhomogeneity. The competition rules for wave patterns (e.g., target waves) are also studied systematically. All the numerical findings are found to be in perfect agreement with the theoretical criteria that are derived based on the fundamental conceptions (e.g., group velocity, phase velocity).     

Traveling wave solutions for a two-species competitive Keller–Segel chemotaxis system

In this paper, the traveling wave problem for a two-species competition reaction–diffusion–chemotaxis Lotka–Volterra system is investigated. Upper and lower solutions method and fixed point theory are employed to show the existence of traveling wave solutions connecting the coexistence constant steady state with zero state for all large enough wave speed $c$, and conversely, when $c$ is small, we prove there is no traveling wave solution.     

Boundedness and persistence of traveling wave solutions for a non-cooperative lattice-diffusion system with time delay

In this paper we study traveling wave solutions of a non-cooperative lattice-diffusion system with time delay, which includes predator–prey models and disease-transmission models. Minimal wave speed of traveling wave solutions is given. Schauder’s fixed-point theorem is applied to show the existence of semi-traveling wave solutions. The boundness and persistence of traveling wave solutions are overcome by using rescaling method and Laplace transform, where the application of Laplace transform to persistence is very novel and creative. The traveling wave solutions for some specific models are shown to connect to a positive equilibrium by using Lyapunov function and LaSalle’s invariance principle.