by using bifurcation theory of planar ordinary differential equations all different bounded travelling wave solutions of the generalized zakharov equation are classified in different parametric regions . in each of these parametric regions the exact explicit parametric representation of all solitary , kink (anti kink) and periodic wave solutions as well as their numerical simulation and thei...

In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and ...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...

We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa-Holm or the Degasperis-Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles.

A reaction-diffusion model for the propagation of an idealized forest fire is revisited to include the effect of wind on the speed of propagation. We study the existence of one-dimensional travelling wave solutions. When the wind velocity is zero or when the wind blows from the burning region, the existence and uniqueness of the travelling wave is proved. In the case when the wind blows into th...

An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the K(2, 2) equation (defocusing branch). Some known results in the literature are recovered more efficiently, and some new exact travelling-wave solutions are obtained. Also, new stationary-wave solutions are obtained.

In this paper, a improved method named the integral bifurcation is introduced. In order to demonstrate its effectiveness for obtaining travelling waves of the nonlinear wave equations, we studied the modified equal width wave equation and its variants by this new method. Under the different parameter conditions, many integral bifurcations are obtained. According to these integral bifurcations, ...

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can th...

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...