In this paper, we employ the exp(-?(x))-expansion method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations Fitzhugh-Nagumo (FN) equation and Modified Liouville equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the proposed method provides...

Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and travel cost (minimized). Applications of these problems arise in contexts such as traveling salesman ...

This article concerns the traveling wave solutions of nonlocal delay reaction-diffusion equations without local quasimonotonicity. The existence of traveling wave solutions is obtained by constructing upper-lower solutions and passing to a limit function. The nonexistence of traveling wave solutions is also established by the theory of asymptotic spreading. The results are applied to a food lim...

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.

Introduction: International travels have increased dramatically in recent years. Adolescents constitute a fast-growing group of travelers. Travels provide an opportunity for exposure to high-risk behavior. The current study reviewed the published data about travel-related morbidity among adolescents traveling to international destinations. Methods: PubMed...

We derive conditions for the existence of traveling wave solutions in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbor interactions and distributed delays. A linear stability analysis of the traveling waves is carried out in terms of perturbations of the firing times of the oscillators. It is shown how traveling waves destabilize when the detuning between oscillator...