The traveling wave equation is an essential tool in the study of vibrations and oscillating systems. This paper introduces an important extension to the Fourier/Laplace transform that is needed for the analysis of signals that are represented by traveling wave equations. Another objective of the paper is to present a mathematical technique for the simulation of the behavior of large systems of ...

A single dispersive element is shown to be sufficient for simultaneous pulse compression and tilting of the pulse front, and therefore well-suited for traveling-wave excitation of targets. It is shown that in all the previous arrangements used for traveling wave excitation, spatially dependent group velocity dispersion occurs along the target. A compensated arrangement is proposed that provides...

Cochlear implant speech processors seek to generate a neural response that mimics normal hearing. However, the cochlear phase response is generally discarded, together with other fine scale temporal aspects of sound. We sought to incorporate and compare a variety of cochlear traveling wave delays (i.e. group delays) in a clinical speech processing strategy. Traveling wave delays resulted in a s...

This paper reviews the efforts to construct (or prove the impossibility of) singular solutions of the Euler equations for three dimensional incompressible flow. A semi-analytic approach to this problem is formulated based on numerical computation of complex traveling wave solutions, followed by perturbation construction of a real solution, for axisymmetric flow with swirl. The perturbation anal...

A generalized ( G′ G ) -expansion method is devised to construct the exact traveling wave solutions of mKdV equation. With the aid of symbolic computation, many hyperbolic function solutions, trigonometric function solutions and rational function solutions are obtained. It is shown that the proposed method is more effective and powerful than the ( G′ G ) -expansion method in constructing the tr...

This paper deals with the existence of traveling wave solutions for m-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction. By using Schauder’s fixed point theorem and a cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained will be applied to...

We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upperand lower solutions. The waves are shown to be unique and strictly monotonic. A KPP wave like asymptotic behaviors are obtained by comparison principle and exponential dichotomy...

In this paper we study the existence of one and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the ...

We consider a model for the interaction of a gas with photons. In the article [10], smooth traveling wave solutions called shock profiles have been constructed under a suitable smallness assumption between the asymptotic states. In this work, we construct piecewise smooth traveling wave solutions that connect two asymptotic states with a large jump. In particular, we give a rigorous mathematica...

033503-1 We present an experimental evidence of a bunch compression scheme that uses a traveling wave accelerating structure as a compressor. The bunch length issued from a laser-driven radio-frequency electron source was compressed by a factor > 3 using an S-band traveling wave structure located immediately downstream from the electron source. Experimental data are found to be in good agreemen...