Yavuz Ugurlu

Solutions of the Cahn-Hilliard equation

In this paper, we found some exact solutions of the Cahn-Hilliard equation and the system of the equations by considering a modified extended tanh function method. A numerical solution to a Cahn-Hilliard equation is obtained using a homotopy perturbation method (HPM) combined with the Adomian decomposition method (ADM). The comparisons are given in the tables.

Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation

Abstract In this paper, we implemented the exp-function method for the exact solutions of the fifth order KdV equation and modified Burgers equation. By using this scheme, we found some exact solutions of the above-mentioned equations.

Comparison of three semi-analytical methods for solving (1+1)-dimensional dispersive long wave equations

In this work, we consider how Adomians decomposition method (ADM), the homotopy analysis method (HAM) and the homotopy perturbation method (HPM) can be used to investigate wave solutions of (1+1)-dimensional dispersive long wave equations. It is also worth noting that the advantage of the approximation of the series methodologies is a fast convergence of the solutions.

Auto-Bäcklund transformation and similarity reductions for coupled Burger’s equation

In this work, we applied Backlund transformation and similarity reduction for coupled Burger’s equation. Clarkson and Kruskal developed a direct and simple method to obtain more similarity solutions of nonlinear partial differential equation. We received our inspiration from Fan’s article, as far as we think that our work is an extended one from the Fan’s has done in his paper. As a result of this study, we obtained solitary wave solutions and traveling wave solutions of coupled Burger’s equation.