Dynamical properties of Schäfer–Wayne equation for propagation of short pulses in silica optical fibers

This research delves into the Schäfer–Wayne equation, a theoretical model that describes the nonlinear propagation of ultra-short pulses in silica optical fibers. The significance of this study lies in our utilization of three distinct analytical techniques to obtain a range of solutions. Additionally, we employ the multiplier approach to calculate conservation laws and identify the Lie point symmetries of the equation. A novel aspect of our investigation is the exploration of periodic, quasiperiodic, and weakly chaotic behaviors of nonlinear optical pulses for the Schäfer–Wayne equation, a topic explored here for the first time. To elaborate on our findings, we provide detailed descriptions of specific solutions. This work contributes to our understanding of the nonlinear dynamics of optical pulses and extends beyond previous efforts in the literature by introducing new analytical methods and uncovering unexplored behaviors within the context of the Schäfer–Wayne equation.