Investigation of optical solitons in a weakly nonlocal Schrödinger equation with parabolic nonlinearity

The weakly nonlinear Schr¨odinger equation (NLSE) describes wave phenomena in media characterized by weakly nonlinear dispersion. As a versatile framework, it finds application across diverse fields such as plasma waves, water waves, fiber optics, and Bose-Einstein condensates, and this study focuses on investigating various solutions for the weakly nonlocal NLSE with parabolic law nonlinearity. By employing the Nucci reduction method (NRM), we extract exact solutions, including dark and bright solitons and other traveling wave solutions. This technique is particularly valuable for identifying nonlocal symmetries of differential equations, providing an efficient analytical tool for nonlinear problem-solving in engineering and related domains. Furthermore, we derive a first integral through the reduction method. These results are essential for understanding soliton wave propagation in weakly nonlocal media with parabolic law nonlinearity, providing insights into wave dynamics for the proposed model. Finally, two- and three-dimensional density plots are presented to illustrate the physical behavior of some obtained solutions within the governing model.

کلیدواژه ها:

Schrödinger model ، parabolic law ، first integral ، Soliton solution ، Nucci method