Analyzing optical solitons in the generalized unstable NLSE in dispersive media

In this research, we utilize innovative methods to successfully address the challenges posed by the generalized unstable nonlinear Schrödinger equation (UNLSE) in dispersive media, yielding a rich array of solutions. Our investigation delves into a wide range of adapted exponential rational function (MERF) techniques, in addition to other unique and valuable approaches. By employing these methodologies in various scenarios, we unveil an extensive variety of wave solutions for the UNLSE. Furthermore, by satisfying specific parameter conditions, we identify novel optical solutions, encompassing both bright and dark solitons within the framework of this equation.