Bifurcation analysis and investigations of optical soliton solutions to fractional generalized third-order nonlinear Schrödinger equation

Abstract This study investigates the optical soliton solutions to the generalized third-order nonlinear Schrödinger equation involving the Caputo fractional derivative using new mapping method. The fractional generalized third-order nonlinear Schrödinger equation is frequently utilized in various fields, including mathematical physics, nonlinear optical phenomena, optical communication technologies and plasma physics. The obtained solutions have different solitons including bell shape, w-shape, anti bell, kink, dark and periodic wave solution. Bifurcation analysis is performed to further explore the behaviour of the system. For this analysis planar dynamical system is obtained by using Galilean transformation. This analysis offers valuable insights into the phase portraits, time series, chaotic behaviour and the sensitivity of the model to the external perturbations. The sensitivity and dynamics of optical solitons are thoroughly investigated that offers significant insights into their behavior within fractional models.