Analytical Solutions and Qualitative Analysis to the Generalized Nonlinear Fractional Schrödinger Model using the Extended Riccati Equation Method

Abstract

The generalized nonlinear Schrödinger equation (GNLSE) has been studied upon the standard nonlinear Schrödinger equation (NLSE) to model how complex wave envelopes change in nonlinear and dispersive environments. There are many applications of the model in the areas like nonlinear optics, plasma dynamics, Bose-Einstein condensates, and surface wave studies. In this investigation, we study exact soliton solutions for the space-time fractional GNLSE using a traveling wave transformation. We apply the extended Riccati equation approach (EREA) to find the analytical solutions like rational, trigonometric, and hyperbolic. Our obtained solutions represents periodic and general solitons. Moreover, we study the bifurcation, chaotic, and sensitivity analysis of the GNLSE.