Obtaining the approximate solutions of some nonlinear equations and examination of obtained solutions

In this thesis, approximate solutions to the real solution of the nonlinear Shrödinger equation are investigated. This study consists of four parts. The first part is the introduction part and the preliminary information about this work is given. In the second chapter, basic concepts related to the subject are given under the title of material and method. Then, the method we applied under the title of residual force series method was introduced. The residual force series method was applied to the Shrödinger equation in four different cases at the beginning of applications of RPSM. In the third chapter, under the title of research findings, the graph of the true solution of the Schrödinger equation is compared with the graph of approximate solutions we find in four different cases. In the final part of the discussion and conclusion, the results obtained here are interpreted. The results show that this method is efficient and useful and can be applied in the form of a major problem. Approximate solutions were compared with known cut-off solutions.