We study entire solutions of a two-component competition system with LotkaVolterra type nonlinearity in a lattice. It is known that this system has traveling wave front solutions and enjoys comparison principle. Based on these solutions, we construct some new entire solutions which behave as two traveling wave fronts moving towards each other from both sides of x-axis.

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only trav...

The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.    

Email: [email protected] Abstract: The enhanced (G′/G)-expansion method is very effective and powerful method to find the exact traveling wave solutions of nonlinear evolution equations. We choose the Phi-4 equation to illustrate the validity and advantages of this method. As a result, many exact traveling wave solutions are obtained, which include soliton, hyperbolic function and trigonom...

In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing. We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. We also construct some new types of entire solutions which are different from the travel...

By using the bifurcation theory of planar dynamical systems to a class of nonlinear evolution equations, the existence of traveling wave solutions is showed. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Explicit exact parametric representations of some traveling wave solutions are obtained.

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of ...

In this manuscript, the existence of traveling-wave solutions to Boussinesq systems  ηt + ux + (ηu)x + auxxx − bηxxt = 0, ut + ηx + uux + cηxxx − duxxt = 0, is established. We prove that all the systems with a < 0, c < 0 and b = d exhibit traveling-wave solutions with small propagation speeds. The result complements our earlier work [6] on a restricted family of the systems where both existenc...

In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α...