Analysis of bifurcation and chaos in the traveling wave solution in optical fibers using the Radhakrishnan–Kundu–Lakshmanan equation

The study examines the propagation of solitary waves in optical fibers controlled by the Radhakrishnan–Kundu–Lakshmanan model (RKL) equation, which includes a cubic–quintic non-Kerr refractive index. The first step in this study involves utilizing the extended algebraic method to derive solitonic solutions for the given equation. These solutions are subsequently graphically represented for a variety of parameter values. The proposed strategy allows for the discovery of a range of solutions.The controlling model is incorporated into a planar dynamical system via the Galilean transformation, resulting in the transformation of the governing model. The effects of both the quintic nonlinearity and self-phase modulation on the perturbed and unperturbed systems are explored using the effective potential and related phase portrait. The governing model is thus transformed into a planar dynamical system. Furthermore, this study harnessed a variety of numerical techniques. These methods encompassed time series analysis, phase portraits examination, and meticulous sensitivity inspections. Additionally, we employed a Poincaré section to assess the equation’s responsiveness to external perturbations. The outcomes reveal a fascinating observation: the perturbed system’s behavior shifts from a quasi-periodic state to a chaotic one, contingent upon the amplitude and frequency of the external perturbation. Moreover, we conducted multistability analysis for specific sets of physical parameters, uncovering the equation’s tendency to exhibit multistability in such scenarios.