Applications of modified double sub-equation method to partial differential equations

In the literature, when recent studies are examined, it is observed that studies contain the wave structures of nonlinear evolution equations are very popular. The main purpose of these studies is to find and analyze traveling wave solution. Various methods have been developed for this purpose. In this master's thesis, complexiton waves which differ from other waves in terms of both velocity and shape, and are combination of trigonometric and exponential functions, were studied. Since complexiton wave contains two different functions, it is structurally different. Therefore it may not be admitted by any evolution equation as a solution. For this reason, it is very difficult to develop exact solution methods that give complexiton solutions. Within the scope of the thesis, at first, wave solutions, homogeneous balance principle, bilinear derivatives and evolution equations were briefly mentioned in order to understand the methods that enable us to reach complexiton wave solutions. In the next section, the modified double sub-equation method and the extended transformed rational function method, which are the main subjects of thesis, were introduced in detail. By using these methods, complexiton solutions of two different nonlinear evolution equations, which are fourth order and (2+1) dimensional, were derived. In addition, the solutions found were visualized with the help of computer for the purpose of being understood easily by readers. Finally, the results were presented and suggestions were shared for studies that can be made on this subject in the future.