Exact solutions to a class of nonlinear wave equations are established using the functional variable method. This method is a powerful tool to the search of exact traveling solutions in closed form.We show that, the method is straightforward and concise for several kind of nonlinear problems. Some specific examples arising in a number of physical problems are displayed using symbolic computer c...

ABSTRACT In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric ...

The homotopy analysis method HAM is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup WBK equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

Khokhlov–Zabolotskaya–Kuznetsov equation (φt + φφx − αφxx)x − 1/2(φyy + φzz) = 0 and its solutions are analyzed. A series of complete exact analytical solutions related to the one-dimensional and vectorial inhomogeneous Burgers equation are presented. A concrete example which corresponds to a special form of the inhomogeneous term is analyzed. Reduction to the traveling wave solution is conside...

In this paper, we investigate the first integral method for solving the K (m,n) equation with generalized evolution. (u)t +a(u )ux +b(u )xxx = 0 A class of traveling wave solutions for the considered equations are obtained where 4n = 3(m + 1). This idea can obtain some exact solutions of this equations based on the theory of Commutative algebra.

In this paper, a variable coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water is presented. With the aid of symbolic computation and using the generalized (G ′ G )-expansion method, the exact traveling wave solutions of this system are obtained. It is shown that t...

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have ...

Abstract The exact traveling wave solutions of generalized Davey-Stewartson equations with arbitrary power nonlinearities are studied using the dynamical system and first integral methods. Taking different parameter conditions, we obtain periodic solutions, solitary kink anti-kink solutions.

A generalized (G ′ /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV equation. As a result, some new Jacobi elliptic function solutions are obtained. It is shown that the method is straightforward, concise, effective, and can be used for many other nonlinear evolution equations in mathematical physics.

In this article, we apply the improved (G′/G)-expansion method to construct some new exact traveling wave solutions including soliton and periodic solutions of the combined KdV-MKdV equation involving parameters. In this method, G′′+λG′+μG = 0 together with ( ) ( ) j m