Optical exact soliton solutions of nonlinear optical transmission equation using two explicit methods

In this research paper, the main aim is to investigate the nonlinear optical transmission equation (NOTE) with two explicit methods. The NOTE is a nonlinear partial differential equation that describes the propagation of light waves in a nonlinear medium, such as an optical fiber or a waveguide. The equation takes into account the effects of dispersion, diffraction, nonlinearity, dissipation, and external potential on the evolution of the complex envelope field of the light wave. The extended \(\Big (\frac{G'}{G^{2}}\Big )\) $(\frac{G^{\prime }}{G^2})$ -expansion method and \(\exp (-\phi (\eta ))\) $exp(-\varphi (\eta ))$ expansion method are successfully applied on the proposed model. The new and novel soliton solutions and other solutions are obtained by the applications of these methods. These solutions include dark soliton, singular soliton, periodic solutions and rational solutions. Constraint conditions for the existence of obtained solutions are also provided in this article. Graphically, the retrieved solutions present different shapes of wave propagations which is shown by 3D graphs. These methods are being applied for the first time on the proposed model and considered as most recent techniques to obtain the soliton solutions for the proposed model.