Özet:
This study presents a novel modification of the Sardar sub-equation method for solving the nonlinear SchrÖdinger equation (NLSE) with second order spatiotemporal dispersion and group velocity dispersion, which is used to describe and model the propagation of optical solitons in nonlinear media. The modification is based on introducing a new function that is used to approximate the solution of the equation. By applying this modified method, we are able to obtain exact analytical solutions for the NLSE with several classes of optical soliton solutions. The method is tested on a variety of nonlinear optical systems and is shown to be highly effective in producing accurate solutions. The results of this study demonstrate the potential of this novel approach for solving the NLSE in the context of optical solitons. These soliton solutions are of great importance in the field of science, physics, mathematics, and engineering.