We study the traveling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painlevé integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of traveling wave solutions can be determined. In some parameter regions, ex...

Electron magnetohydrodynamics (EMHD) provides a fluidlike description of small-scale magnetized plasmas. An EMHD wave propagates along magnetic field lines. The direction of propagation can be either parallel or antiparallel to the magnetic field lines. We numerically study propagation of three-dimensional (3D) EMHD wave packets moving in one direction. We obtain two major results. (1) Unlike i...

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G′/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expr...

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-B...

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator–prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator– prey system in the traveling wave variable. ...

Transmission lines are designed to transfer electric power from source locations to distribution networks. This project investigates the problem of fault localization using traveling wave voltage and current signals obtained at a single end of a transmission line and multi ends of a transmission network. Fourier transform (FT) is the most popular transformation that can be applied to traveling ...

This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse ...

Traveling-wave-based fault location in electrical distribution systems is an important safeguard for the distribution network reliability. The effectiveness of the methods is verified directly in power grid in the early stages, while different fault types can't appear in a short time. And normal dynamic physical simulation cannot meet the teaching demand either because of the limitation of tran...

Current models of evoked otoacoustic emissions explain the striking periodicity in their frequency spectra by suggesting that it originates through the reflection of forward-traveling waves by a corresponding spatial corrugation in the mechanics of the cochlea. Although measurements of primate cochlear anatomy find no such corrugation, they do indicate a considerable irregularity in the arrange...

In this paper, an extended elliptic equation expansion method is presented for constructing exact traveling wave solutions of nonlinear partial differential equation. The main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact traveling wave solutions of nonlinear partial differential equations. The ZK-MEW equation is chosen to illustrate ...