Investigation of exact solutions of nonlinear mathematical models by analytical method

The exponential function method was introduced by Ji-Huan He and Xu-Hong Wu in 2006 for nonlinear partial differential equations, whose solutions are very difficult to obtain, and wave solutions of the equations were found by applying this method to many equations over the years. A relatively short time ago, with the acceptance function included in the method being discussed more comprehensively, its final improved form, that is, the modified exponential function method, came to light. In this thesis study, traveling wave solutions of the equations were obtained by applying the modified exponential function method for the first time in the literature to some nonlinear partial differential equations encountered in various scientific research. In addition, the physical structure of the solutions offered by the method is presented with visuals and their similarities and differences with the solutions offered by other solution methods in the literature to the mentioned equations are investigated.