Optical solitons and modulation instability analysis for the generalized resonant dispersive nonlinear Schrödinger equation with dual power-law nonlinearity

For systems modeled by the resonant nonlinear Schrödinger equation, we aim to investigate the soliton dynamics and the stability of the system. We extend the equation to a generalized form (GRD-NLSE) and utilize the modified F-expansion method to derive various soliton solutions, including bright, kink, and singular solitons for both (1 + 1)-dimensional and (2 + 1)-dimensional models. Additionally, we graphically illustrate soliton behavior. To analyze system stability, we perform modulation instability and soliton stability analyses. Our findings provide valuable guidance for experimental studies and observations of solitons in GRD-NLSE systems.