Abstract
Solitons which can be described as a localized wave form that maintain their shape after a collision with another soliton have became a very important phenomena in nonlinear optics due to their potential. They can be used as lossless information carriers in optical fibers due to their robustness arising from their particle grade stability upon a collision. Many scientists from various areas including electronic communication engineers have made solitons the main subject of study. Analytical solutions of nonlinear Schrödinger equation have a very important place in these studies. With the progress of nonlinear optics, some types of nonlinear Schrödinger equation have been derived for better understanding. Resonant nonlinear Schrödinger equation which is being used for describing nonlinear optical phenomena is a generic example for newly derived nonlinear Schrödinger equation. In this study, resonant nonlinear Schrödinger equation has been solved by using functional variable method and sixteen new soliton solutions have been obtained
Mathematical analysis of adaptive step-size techniques when solving the nonlinear Schrödinger equation for simulating light-wave propagation in optical fibers
