A simple model is studied for the chemotactic movement of biological cells in the presence of a periodic chemical wave. It incorporates the feature of adaptation that may play an important role in allowing for “rectified” chemotaxis: motion opposite the direction of wave propagation. The conditions under which such rectification occurs are elucidated in terms of the form and speed of the chemic...

The purpose of this paper is to study traveling wave fronts of a two-dimensional (2D) lattice delayed differential equation with global interaction. Applying the comparison principle combined with the technical weighted-energy method, we prove that any given traveling wave front with large speed is time-asymptotically stable when the initial perturbation around the wave front need decay to zero...

We have presented a new hyperbolic auxiliary function method for obtaining traveling wave solutions of nonlinear partial differential equations. Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed.

Introduction At high magnetic field strengths, travelling wave MRI can be used to solve the standing wave problem of volume resonators [1]. However, travelling wave MRI suffers from electromagnetic field-attenuation and high whole body energy deposition (SAR), so that only the distal parts of the body can be imaged. In this work we introduce a new travelling wave RF coil. The coil guides the tr...

The theory, design and experimental results of a wideband 140 GHz, 1 kW pulsed gyro-traveling wave amplifier are presented. The gyro-TWA operates in the HE(0,6) mode of an overmoded quasi-optical waveguide using a gyrating electron beam. The electromagnetic theory, interaction theory, design processes and experimental procedures are described in detail. At 37.7 kV and 2.7 A beam current, the ex...

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the ( G′ G ) -expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic so...

In this article, we apply the Multiquadric radial basis function (RBF) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the Kawahara equation. The scheme is based on the Crank-Nicolsonformulation for space derivative. The performance of the method is shown innumerical examples.

By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green–Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric rep...

and Applied Analysis 3 25 , the traveling wave solution of 1.2 is a damped oscillatory solution which has a bell profile head. However, they did not present any analytic solution or approximate solution for 1.2 . Xiong 25 obtained a kink profile solitary wave solution for KdV-Burgers equation. In 26 , S. D. Liu and S. D. Liu obtained an approximate damped oscillatory solution to a saddle-focus ...

Abstract A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic modeling, i.e., the Boltzmann transport equation, and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopi...