Solitonic, quasi-periodic, super nonlinear and chaotic behaviors of a dispersive extended nonlinear Schrödinger equation in an optical fiber

Abstract

Various dynamic behaviors of the dispersive extended nonlinear Schrödinger equation (NLSE) are studied in this paper. For this, a new Φ6−model expansion method is used to examine the solitary waves of the considered model. The main objective of this approach is to provide a medium by involving various parameters for Jacobian elliptic solutions. It is also noted that certain bright–dark optical solitons are given by the NLSE, as well as bell-shaped bright optical solitons. By applying Galilean transformation to evaluate the nonlinear and super nonlinear periodic behaviors in nonlinear optics, the system is transformed into a planar dynamical system. By using phase portrait analysis, we first investigate the presence of a set of novel optical solitons of the NLSE. The dynamic motions for the nonlinear, super nonlinear, periodic, quasi-periodic and chaotic motions are studied using various parametric conditions in the presence of external periodic force. Bifurcation analysis and sensitivity analysis for NLSE propagation is represented using phase plane analysis via phase plots of the dynamic structure. Further, via time series plots, we present analytical forms of the solitary waves.