Mohammed Khalfallah

Exact traveling wave solutions of the Boussinesq-Burgers equation

The extended homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq-Burgers equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Boussinesq-Burgers equation are successfully obtained.

The homogeneous balance method and its application to the Benjamin–Bona–Mahoney (BBM) equation

Abstract We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the Benjamin–Bona–Mahoney (BBM) equation. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations.

New periodic wave and soliton solutions for system of coupled Korteweg-de Vries equations

The periodic wave solutions for the system of coupled Korteweg-de Vries equations are obtained by using of Jacobi elliptic function method, in the limit cases, the multiple soliton solutions are also obtained. The properties of some periodic and soliton solution for this system are shown by some figures.

Multi soliton solution for the system of Coupled Korteweg-de Vries equations

In this paper we consider the system of coupled Korteweg-de Vries equations and establish the transformation which turns the coupled KdV equations into the single nonlinear partial differential equation, then we obtain an auto-Backlund transformation and Lax pairs by using the extended homogeneous balance method. Also, we obtain the multi soliton solutions and the new trigonometric function periodic solutions by using the generalized tanh method.