Some special methods in solving partial differential equations

In this thesis work, some special methods for solving partial differential equations are considered. These methods are tanh-coth method and the sn-ns method. Outline of these methods are given, respectively. The tanh-coth and the sn-ns methods are applied to Benjamin-Bona-Mahony equation. Then, the solutions of this partial differential equation are found by using these methods. Firstly, we obtain the solutions of BBM equation by using tanh-coth and the sn-ns methods. After that, we compare the solutions gained by both methods. It is seen that the solutions found by the sn-ns methods always contains the ones found by the tanh-coth method. Therefore, it is shown that the tanh-coth method is a special case of the sn-ns method. According to findings in this work, the sn-ns method is more comprehensive then the tanh-coth method in finding the general solutions of partial differential equations and gives more solutions.