Traveling wave solutions for a non-monotone Logistic equation in a cylinder

The traveling wave solutions connecting two equilibria for a delayed Logistic equation in a cylinder are obtained for any delay $\tau >0$. We attain our goal by using the approach based on the combination of Schauder fixed point theory and the weak coupled upper–lower solutions method. Moreover, we prove that there is a constant $c^1$ that serves as the minimal wave speed of such traveling wave solutions.     

Exact Solitary Wave And Periodic Wave Solutions Of The Kaup-Kuperschmidt Equation

In this paper we investigate the exact traveling wave solutions of the fifth-order Kaup-Kuperschmidt equation. The bifurcation and exact solutions of a general first-order nonlinear equation are investigated firstly. With the help of Maple and by using the bifurcation and exact solutions of two derived subequations, we obtain two families of solitary wave solutions and two families of periodic wave solutions of the KK equation. The relationship of the two subequations and the two known rst integrals are analyzed.     

Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation

In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.     

Spreading speeds and traveling waves for a time periodic DS-I-A epidemic model

This paper is devoted to studying the speed of asymptotic spreading and minimal wave speed of traveling wave solutions for a time periodic and diffusive DS-I-A epidemic model, which describes the propagation threshold of disease spreading. The main feature of this model is the possible deficiency of the classical comparison principle such that many known results do not directly work. The speed of asymptotic spreading is estimated by constructing auxiliary equations and applying the classical theory of asymptotic spreading for Fisher type equation. The minimal wave speed is established by proving the existence and nonexistence of the nonconstant traveling wave solutions. Moreover, some numerical examples are presented to model the propagation dynamics of this system.     

浅水波方程和Klein-Gordon方程新的精确行波解

采用了一种新的方法来求解浅水波方程和Klein-Gordon的行波解.在该方法下,Klein-Gordon方程和浅水波方程都得到了其精确的周期孤立波解,从而该方法的有效性得到了验证.     

Traveling wave solutions in a diffusive system with two preys and one predator

This paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator. By constructing upper and lower solutions, the existence of nontrivial traveling wave solutions is established. The asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles. Applying the theory of asymptotic spreading, the nonexistence of traveling wave solutions is proved.     

Nagumo方程行波系统的定性分析及其有界行波解

本文对Nagumo方程的行波系统进行了定性分析,该系统存在一端连接鞍点的有界异宿轨,进而选择奇点为鞍点的平面线性自治系统,利用该平面自治系统轨线向径的斜率,根据齐次平衡原则,构造出了Nagumo方程行波系统的行波解.其次Nagumo方程的行波系统还存在着对应中心周围闭轨的周期解,因而提出新的CPP解法,求出了对应的周期解.     

一个交通模型的行波解的渐近稳定性

主要考虑下面的交通模型的行波解的渐近稳定性.{vt-ux=0 (E)ut+p(v)x=1/ε(f(v)-u+μuxx 其中初始值为 (v,u)(x,0)=(v0(x),u0(x))→(v±,u±),v±＞0,as x→±∞.(Ⅰ)在允许流函数f不是凹函数以及初始值在无穷远处的极限不满足平衡方程的条件下,我们得到了稳定性...     

Traveling Wave Fronts of a Degenerate Parabolic Equation with Non-divergence Form

We study the traveling wave solutions of a nonlinear degenerate parabolic equation with non-divergence form. Under some conditions on the source, we establish the existence, and then discuss the regularity of such solutions.     

一些非线性发展方程的显式行波解

该文给出了一种构造非线性发展方程显式行波解的方法并用该方法得到了Hirota-Satsuma方程组,一类非线性常微分方程以及广义耦合标量场方程组的显式行波解.     

对称正则长波方程的行波解分岔

通过平面动力系统的方法讨论了对称正则长波方程的分岔问题.得到了该方程的分岔条件,在一些参数的具体值的情况下给出相图并通过微分方程的数值模拟方法模拟出了该方程的周期行波解、孤立行波解及无界行波解.     

Traveling waves for a periodic Lotka–Volterra predator–prey system

This paper is concerned with the time periodic traveling wave solutions for a periodic Lotka–Volterra predator–prey system, which formulates that both species synchronously invade a new habitat. We first establish the existence of periodic traveling wave solutions by combining the upper and lower solutions with contracting mapping principle and Schauder’s fixed point theorem. The asymptotic behavior of nontrivial solution is given precisely by the stability of the corresponding kinetic system that has been widely investigated. Then, the nonexistence of periodic traveling wave solutions is confirmed by applying the theory of asymptotic spreading. We show the conclusion for all positive wave speed and obtain the minimal wave speed.     

一类带时滞和全局反应项生物模型的行波解

研究了带时滞的微分方程异宿轨解的存在条件,并通过时滞微分系统和反应扩散系统解之间的关联性,得到了一类带全局反应项的生物反应扩散模型的行波解.     

Traveling Wave Solutions in a Chemotaxis Model with Two Chemoattractants

In this work, we investigate the existence and non-existence of traveling wave solutions for a chemotaxis model with two chemoattractants. To prove our main results, we apply the dynamical systems theory by constructing a positively invariant set in the four-dimensional space. Particularly, we analyze the monotonicity of traveling wave solutions.     

一类二次KdV类型水波方程的行波解

应用平面动力系统理论研究了一类非线性KdV方程的行波解的动力学行为．在参数空间的不同区域内,给出了系统存在孤立波解,周期波解,扭子和反扭子波解的充分条件,并计算出所有可能的精确行波解的参数表示．     

Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.     

Traveling wave fronts in a delayed lattice competitive system

This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness.     

Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.     

广义的Zakharov方程和Ginzburg-Landau方程的精确解和行波解分支

获得了广义的Zakharov方程和Ginzburg-Landau方程的一些精确行波解,这些行波解有什么样的动力学行为,它们怎样依赖系统的参数？该文将利用动力系统方法回答这些问题,给出了两个方程的6个行波解的精确参数表达式．     

Existence and Nonexistence of Traveling Wave Solutions for a Bistable Reaction-Diffusion Equation in an Infinite Cylinder Whose Diameter is Suddenly Increased

ABSTRACT

We consider a reaction-diffusion equation of bistable type in a square cylinder whose diameter varies with Neumann boundary conditions in dimension 2 and 3. We prove the nonexistence of generalized traveling wave solution of this equation when the diameter is suddenly strongly increased. At the same time, we prove that the solution of the equation with an exponentially decreasing initial condition cannot pass over a certain threshold far enough in the direction of propagation.

The proof is divided in two steps. First, we extend the solution in the cylinder to a solution of the same equation in the half space. Then we overestimate it using Green's functions.