We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D lattice equations with non-monotone birth functions. First, with the help of Ikehara’s Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier res...

The cubic complex one-dimensional Ginzburg–Landau equation is considered. Using the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave no elliptic travelling wave solution. This result amplifies the Hone’s result, that this equation has no elliptic travelling wave solution.

A travelling waves analysis for a polyatomic gas with n internal energy storage modes is performed. In both the frozen ow and the equilibrium limit the existence and the qualitative behaviour of travelling waves are investigated. Methods from geometric singular perturbation theory are used to study these limits.

Various monitoring and performance evaluation tools generate considerable amount of low priority traffic. This information is not always needed in real time, and thus could often be delayed by the network without hurting functionality. This paper proposes a new framework to handle this low priority, but resource consuming traffic in such a way that it will incur a minimal interference with the ...

An overview of various aspects related to the spectral and nonlinear stability of travelling-wave solutions to partial differential equations is given. The point and the essential spectrum of the linearization about a travelling wave are discussed as is the relation between these spectra, Fredholm properties, and the existence of exponential dichotomies (or Green’s functions) for the linear ope...

There exists no “one size fits all” approach to planning education in Europe (Healey 2011; Kunzmann 2015; Kunzmann, Schretzenmayr 2015; Gilliard, Thierstein 2015; Alterman 2016). A European-wide planning education approach seems neither possible nor desirable. Not possible because “Europe has many quite different regional traditions when it comes to educating planners” and “there does not seem ...

In this paper, we introduce a generalization of travelling waves for evolution equations. We are especially interested in reaction-diffusion equations and systems in heterogeneous media (with general operators and general geometry). Our goal is threefold. First we give several definitions, for transition waves, fronts, pulses, global mean speed of propagation, etc. Next, we discuss the meaning ...

The Traveling Salesman Problem (TSP) is a classical problem in discrete optimization. Its paradigmatic character makes it one of the most studied in computer science and operations research and one for which an impressive amount of algorithms (in particular heuristics and approximation algorithms) have been proposed. While in the general case the problem is known not to allow any constant ratio...

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In this work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclini...

In this paper, we develop a hydraulic theory to describe the occurrence and structure of slugging in a confined two-layer gas–liquid flow generated by prescribed, constant, upstream volumetric flow rates in each layer. A linearized theory for the uniform flow is established, after which we use bifurcation theory to study fully non-linear periodic travelling wave structures. We find that a two-p...