Novel soliton wave solutions of a special model of the nonlinear Schrödinger equations with mixed derivatives

In this study, the influence of the integrability requirement on nonlinear Schrödinger equations with mixed derivatives is examined. The Rangwala–Rao (RR) equation is named after A. Rangwala, who in 1990 was the first to quantify these effects in their entirety. The aim of our research is identifying how to generate individual waves and how they interact with one another. This is to get a better understanding of the dispersion effect and the progressive variation of the electric field envelope during pulse propagation in optical fibers. The direct algebraic method (DAM), the extended direct algebraic approach (exDAA), and the extended Riccati expansion technique (exREM) are used to develop unique solitary wave solutions for the model under consideration. These numerically calculated solutions illustrate the dynamic behavior of an optical pulse traveling through a cable. Comparing our results to those of other researchers demonstrates the originality of our work.