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.

in this paper, the operation of helix traveling wave tube in interaction region is investigated by using a three dimensional large signal lagrangian model in frequency domain. the complete simulation of these tubes is essential for optimum design and minimum manufacturing cost. this 3d code can compute interception current (or current losses ), beam radius changes in interaction region and the ...

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...

This paper is concerned with Nicholson’s blowflies equation, a kind of time-delayed reaction-diffusion equation. It is known that when the ratio of birth rate coefficient and death rate coefficient satisfies 1 < p d ≤ e, the equation is monotone and possesses monotone traveling wavefronts, which have been intensively studied in previous research. However, when p d > e, the equation losses its m...

In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(|u|u)xx for p > 1, a ≥ b > 0. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms uxxxx and uxxtt. We obtain an explicit condition in terms of a, b and p on wave...

The spatial and temporal periodicity of somite formation is controlled by the segmentation clock, in which numerous cells cyclically express hairy-related transcriptional repressors with a posterior-to-anterior phase delay, creating 'traveling waves' of her1 expression. In zebrafish, the first traveling wave buds off from the synchronous oscillation zone in the blastoderm margin. Here we show t...