Exact solutions of some nonlinear partial differential equations with different types of Kudryashov method

In mathematics, equations that relate one or more functions and their derivatives are called differential equations. Differential equations have an important place in mathematics because they are an effective tool for solving mathematical problems. Therefore, exact solutions of differential equations have been investigated in the field of applied mathematics within the department of mathematics. Some methods have been proposed and included in the literature to find exact solutions of differential equations. In this thesis, different types of Kudryashov's method, which is one of these methods, and exact solutions of some nonlinear partial differential equations have been investigated. The Kudryashov method is one of the effective methods used in the search for exact solutions of nonlinear differential equations, presented by N. A. Kudryashov. There are many types of the Kudryashov method in the literature. In this thesis, generalized and new Kudryashov methods have been used to find solutions of some nonlinear partial differential equations. The Drinfeld-Sokolov-Wilson system of nonlinear partial differential equations and the Kolmogorov-Petrovskii-Piskunov, simplified modified Camassa Holm, Sawada- Kotera and Kaup-Kupershmidt equations, which are derivatives of the Kudryashov method, were studied for exact solutions. The partial differential equations were reduced to ordinary differential equations using moving wave transformations and the solutions of these ordinary differential equations were studied with the solution algorithm of the methods used. The solutions found were supported with 3-dimensional, contour and density graphics with the help of Maple software. The solutions obtained in this thesis study showed that the generalized and new Kudryashov methods are an effective tool in finding exact solutions of the given nonlinear partial differential equations. The ability to solve the differential equations given by these methods indicates that the generalized and new Kudryashov methods are applicable and maintain their importance in adding new exact solutions to the literature.