Self-steepening nature and nonlinearity management of optical solitons with the influence of generalized external potentials

A nonlinear Schrödinger equation with the combined effects of variable nonlinearity and generalized external potentials is investigated. Three soliton solutions are generated by means of Darboux method through constructed Lax pair. We attained two constraints related to gain or loss function for considered equation via compatibility condition. Using three soliton solutions, influences of the inhomogeneous nonlinearity and harmonic potential on soliton structures are analysed by properly tailoring the loss or gain parameter. Specifically, via inelastic collision among three solitons, soliton switching characteristics is observed. Additionally, we explore the Modulation instability (MI) through linear stability analysis (LSA) and impact of nonlinearity profile is examined. The trigonometric, exponential and constant values have been chosen for loss or gain parameter to study the effect on the MI gain spectrum.