The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...

Solitary-wave solutions of a nonlinearly dispersive equation are considered. It is found that solitary waves are peaked or smooth waves, depending on the wave speed. The stability of the smooth solitary waves also depends on the wave speed. Orbital stability is proved for some wave speeds, while instability is proved for others.

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

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.    

ABSTRACT The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain soli...

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when selfinteraction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrödinger equations with repulsive self-interacti...

The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitra...

In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurance of such a spurious solitary wave, which exhibits a very long life time, results in a nonvanis...

I investigated a Bose–Einstein condensate confined harmonically to 1D, within the framework of Gross–Pitaevskii mean–field theory. I consider the 1D Gross–Pitaevskii equation with a combined step in its external potential and nonlinear terms. I generalise solitary wave solutions to the equation in its nonlinear limit, to take into account a constant potential and nonlinearity. I then generalise...