Finding exact solutions of some partial differential equations with modified trial equation method

This study consists of five chapters. The first part is the introduction, which gives informations about the partial differential equations and the historical development of the modified trial equation method. In the second part, some basic definitions and concepts required fort his thesis are qiven. In the third part, the general structure of the modified trial equation method is introduced. In the fourth section, Modified trial Equation method is applied to these equations to find some exact solutions of Laksmanan-Porsezian-Daniel (LPD), Van der Waals, (2+1) Dimensional ZakharovKuznetsov, Chafee-Infante, (2+1) Dimensional Broer-Kaup Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) equations. Also, two and three dimensional graphics of the solutions obtained with the help of Mathematica 9 program are drawn. The fifth part is the conclusion part and camprehensive results about the solutions obtained in this thesis are given.