Nonlinear partial differential equations and exact solutions

In this thesis, some evolution type ((1)+(1), (2)+(1) and (3)+(1) dimensional) nonlinear real and complex partial differential equations are considered. These equations are nonlinear mathematical models that describe many physical phenomena in various disciplines. Analytical exact solutions of these equations were tried to be obtained. In this context, Kudryashov and tanh function methods, which are extensively studied and developed in the literature, are discussed. These methods were applied separately to the physical models considered. In addition, the Hirota approach based on the bilinearization of nonlinear equations was examined. In order to alleviate some of the difficulties in this approach, we investigated how multiple soliton solutions were obtained by using the proposed simplified Hirota method. In the last part of our study, Lie group approach, which does not require any restriction on the order, degree or linearity properties of the equation, is discussed. Comparisons of the obtained results, physical meanings of the solution types and graphical structures of the solutions were also demonstrated.