Analytical solutions of the some nonlinear schrödinger equation with the extended direct algebraic method

In the field of applied mathematics, nonlinear partial differential equations have a very important place due to their theoretical and practical applications. Many methods have been developed to solve nonlinear structures that are of such importance. The extended direct algebraic method, which is a current method, is a very effective method to obtain analytical solutions of nonlinear differential equations. Our thesis designed for this purpose is; In the first chapter, the concept of Soliton, which occurs in the solutions of non-linear partial differential equations and is one of the basic concepts of our thesis, is mentioned. A general information is given on the studies carried out on this subject. In the second part, the definitions of the generalized hyperbolic functions that we will use in the extended direct algebraic method are given. In the third section, information is given about the general structure of the extended direct algebraic method that we will use and its application to equations. In the fourth chapter, analytical solutions of the extended nonlinear Schrödinger equation are obtained by the discussed method. Finally, a general evaluation was made with the results obtained.