Optical solitons retrieval for an extension of novel dual-mode of a dispersive non-linear Schrödinger equation

In this study, we rearrange the non-linear Schrödinger equation (NLSE) into a dual-mode structure, which expands it, and then we investigate the geometrical evaluation and representation of this novel model. Explicit, exact solutions are obtained by implementing the improved modified extended tanh-function (IMETF) approach. The study’s findings have important ramifications for how solitons propagate in nonlinear optics. The resultant solutions can be found in several forms: singular, bright, rational, exponential, Jacobi elliptic function (JEF), Weierstrass elliptic doubly periodic solution, and singular periodic solutions. By comparing our obtained traveling wave solutions with existing literature, we demonstrate their novelty and substantive contribution to current research. The success of our approach suggests its potential applicability to address various nonlinear challenges in different fields, particularly within soliton theory, since the analyzed model appears in a multitude of applications. Besides, in order to better comprehend some of these found solutions behaviors, we showed their outlines in 3D and 2D graphs.