Dynamical analysis, chaos and multistability of the resonant third-order nonlinear Schrödinger equation through phase portraits

The main aim of this paper is to navigate qualitative research to deal with chaotic behavior, bifurcation, and sensitivity analysis through phase diagrams. The model under consideration is a resonant third-order nonlinear Schrödinger equation describing wave propagation in fiber optics. The equation is converted into nonlinear ordinary differential equations using a traveling wave hypothesis, which utilizes the Galilean transformation to turn into a planar dynamical system. Further, the qualitative dynamics of the time-dependent dynamical system are investigated using chaos theory. The phase portraits, time series, Poincaré maps and Lyapunov exponent are used to identify chaotic behavior in self-governing dynamical systems. Four distinct initial conditions are used to examine the model’s sensitivity. Additionally, soliton solutions examined include bright envelope soliton solutions, dark envelope soliton solutions and periodic solutions with their existence criterion.