Bifurcations, chaotic dynamics, sensitivity analysis and some novel optical solitons of the perturbed non-linear Schrödinger equation with Kerr law non-linearity

This study introduces an analysis of bifurcations, chaotic dynamics, and sensitivity using the Galilean transformation applied to the perturbed non-linear Schrödinger equation (NLSE) with Kerr-law nonlinearity. Additionally, we employ the efficient Sardar sub-equation (Sse) method to derive various optical soliton solutions. Initially, we outline the general framework of the Sse method proposed. Next, we utilize a traveling wave transform on the NLSE, transforming it into a system of nonlinear ordinary differential equations (NLODEs) which are further separated into their real and imaginary components. Furthermore, we apply this method to derive new optical solitons for the NLSE equation with Kerr law. We perform exact analytical simulations of these optical soliton solutions and investigate the effects of different parameters on the soliton waves.