Analysis of soliton solutions of some nonlinear partial differential equations by modified exponential expansion function method

Partial differential equations are used in modeling many real-life events. For this reason, there are different studies in the literature on the solutions of partial differential equations. Among these studies, especially the wave equations and their solutions were focused on. The most important reason for this is that wave equations have a wide application area in the mathematical modeling of natural events and phenomena. For example, many physical processes such as sound, heat, and electromagnetic waves can be explained by wave equations. Within the scope of this thesis, some partial differential equations available in the literature are discussed and their analytical solutions are examined with the modified exponential function expansion method. For this purpose, firstly, in the first and second parts of the thesis, a general literature review is given and the basic definitions and concepts to be used in the next sections are expressed. In the third chapter, the modified exponential function expansion method, which will be used to investigate the analytical solutions of the partial differential equations, is introduced and the steps of the method are explained in detail. Finally, analytical solutions of modified Burgers KdV, Benjamin-Bono-Mahony, and modified Korteweg-de Vries (KdV) equations are characterized and visualized by plotting contour plots with graphs of various dimensions.