Analysis of wave solutions of non-linear partial differential equations

In this thesis, the traveling wave solutions of the nonlinear partial differential equations, Mikhailov-Novikov-Wang Equation and Kairat-II Equation, are analyzed using the modified exponential function method. The solution functions are obtained through a mathematical program. Two-dimensional, three-dimensional, contour, and precision graphs illustrating the behavior of the traveling wave solutions representing the mathematical model have been plotted using suitable parameters via a software package. It has been demonstrated that the method used for finding the solution functions of the Mikhailov-Novikov-Wang and Kairat-II equations is a more convenient approach. Solutions for the Mikhailov-Novikov-Wang equation have been obtained, and two-dimensional, three-dimensional, precision, and contour graphs have been drawn. However, for the Kairat-II equation, not all solution functions yielded results, and their graphs could not be plotted. In the first section of the study, information is presented about the fields of science that interact with nonlinear partial differential equations and the areas of their application, along with a detailed examination of the specific equations addressed. The second section includes the necessary definitions relevant to the study. In the third section, the methods employed in the thesis are introduced and examined in detail. The fourth section applies the modified exponential function method to the equations analyzed, resulting in traveling wave solutions. Graphics for two-dimensional, threedimensional, boundary, and precision analyses are generated using software. The fifth section compares the employed method with other techniques applied to these equations and evaluates the results of the solution functions.