Traveling Wave Solutions in an Integrodifference Equation with Weak Compactness

This article studies the existence of traveling wave solutions in an integrodifference equation with weak compactness. Because of the special kernel function that may depend on the Dirac function, traveling wave maps have lower regularity such that it is difficult to directly look for a traveling wave solution in the uniformly continuous and bounded functional space. In this paper, by introducing a proper set of potential wave profiles, we can obtain the existence and precise asymptotic behavior of nontrivial traveling wave solutions, during which we do not require the monotonicity of this model.     

A Tabu Search Approach for the Prize Collecting Traveling Salesman Problem

The Prize Collecting Traveling Salesman Problem is a generalization of the Traveling Salesman Problem. A salesman collects a prize for each visited city and pays a penalty for each non visited city. The objective is to minimize the sum of the travel costs and penalties, but collecting a minimum pre-established amount of prizes. This problem is here addressed by a simple, but efficient tabu search approach which had improved several upper bounds of the considered instances.     

New neighborhood structures for the Double Traveling Salesman Problem with Multiple Stacks

The changing requirements in transportation and logistics have recently induced the appearance of new vehicle routing problems that include complex constraints as precedence or loading constraints. One of these problems that have appeared during the last few years is the Double Traveling Salesman Problem with Multiple Stacks (DTSPMS), a vehicle routing problem in which some pickups and deliveries must be performed in two independent networks, verifying some precedence and loading constraints imposed on the vehicle. In this paper, four new neighborhood structures for the DTSPMS based on reinsertion and permutation of orders to modify both the routes and the loading planning of the solutions are introduced and described in detail. They can be used in combination with any metaheuristic using local search as a subprocedure, guiding the search to unexplored zones of the solution space. Some computational results obtained using all proposed neighborhood structures are presented, providing good quality solutions for real sized instances.      

Reoptimization of minimum and maximum traveling salesman's tours

In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5-approximation algorithm for the reoptimization version of MaxTSP.     

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.     

A numerical investigation of blow-up in reaction-diffusion problems with traveling heat sources

This paper studies the numerical solution of a reaction-diffusion differential equation with traveling heat sources. According to the fact that the locations of heat sources are known, we add auxiliary mesh points exactly at heat sources and present a novel moving mesh algorithm for solving the problem. Several examples are provided to demonstrate the efficiency of the new moving mesh method, especially in the case of two or three traveling heat sources. Moreover, numerical results illustrate that the speed of the movement of the heat source is critical for blow-up when there is only one traveling heat source. For the case of two traveling heat sources, blow-up depends not only on the speed but also on the distance between the two traveling heat sources.     

Modified Tunneladder Slow-Wave Structures for High-Power Millimeter-Wave TWTs

In this paper, five modified Tunneladder slow-wave structures (SWS), the ridge-loaded stub-supported meander line with circular electron tunnel (CET-RSML), ring-plane frame line (RPFL), the ridge-loaded thick ladder line (RLTLL), the ridge-loaded pole-piece folded-waveguide circuit (RLPFWL), and the double-period Tunneladder line (DPTL) were discussed. The dispersion characteristics and the interaction impedances of the five modified Tunneladder SWS were calculated by simulation and the corresponding analytic models. The calculation results explain that the CET-RSML and the RLTLL hold wider bandwidth in comparison with the Tunneladder, when the volume dimensional lengths are same. When the bandwidth is definite, the interaction impedance of RLTLL can be higher than Tunneladder, but that of CET-RSML can’t. The dispersion curves of the RLPFWL and the DPTL are more linear in comparison with Tunneladder, but the interaction impedances are very low. Supported by the National Natural Science Foundation of China, under Grant No. 60532010.     

Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Elimination of Anti-spiral Waves by Local Inhomogeneity in Oscillatory Systems

Anti-spiral waves are controlled in an oscillatory system by using a local inhomogeneity. The inhomogeneity acts as a wave source, and gives rise to the propagating plane waves. It is found that there is a critical pacemaking domain size below which no wave will be created at all. Two types of ordered waves (target waves and traveling waves) are created depending on the geometry of the local inhomogeneity. The competition between the anti-spiral waves and the ordered waves is discussed. Two different competition mechanisms were observed, which are related to the ordered waves obtained from different local inhomogeneities. It is found that traveling waves with either lower frequency or higher frequency can both eliminate the anti-spiral waves, while only the target waves with lower absolute value of frequency can eliminate the anti-spiral waves.This method also applies to outwardly rotating spiral waves. The control mechanism is intuitively explained and the control method is easily operative.