Grey and black optical solitary waves, and modulation instability analysis to the perturbed nonlinear Schrodinger equation with Kerr law nonlinearity

This paper addresses the nonlinear Schrodinger equation (NLSE) with Kerr law nonlinearity and perturbation terms in optical fibre. A class of grey and black optical solitary wave solutions of this equation are retrieved by adopting an appropriate solitary wave ansatz solution. These types of solitary waves play a vital role in understanding various physical phenomena in nonlinear systems. This lead to a constraint condition on the solitary wave parameters which must hold for the solitary waves to exist. Moreover, the modulation instability (MI) analysis of the model is studied by employing the concept of linear-stability analysis (LSA) and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviours of the equation.