Optical soliton perturbation, phase portrait and sensitivity analysis in birefringent fibers with the stochastic complex Ginzburg-Landau equation having cubic-quintic-septic-nonic nonlinearities

Abstract

Optical soliton solutions, chaotic behaviors and bifurcation analysis of the perturbed complex Ginzburg-Landau equation having non-Kerr law media with the effect of multiplicative white noise in birefringent fibers are researched, for the first time, in this study. Perturbation terms of the Hamiltonian type and cubic-quintic-septicnonic form of self-phase modulation are taken into consideration. Two integration schemes, namely the extended trial function algorithm and the extended (G′/G)-expansion technique are applied to reveal a variety of wave profiles such as bright, dark and singular soliton solutions, rational waves and periodic solutions to the governing equation. Existence criteria of the soliton solutions are also provided. In addition 2D, 3D and contour figures are presented to illustrate dynamic behaviour of the solutions. Moreover, by virtue of the traveling wave hypothesis, the model is turned into a two-dimensional dynamical system. Then, the behaviors of this system and its periodic disturbance system are analyzed in detail utilizing methods such as equilibrium point analysis, time series, phase portraits, Poincaré sections and sensitivity to initial conditions to verify the presence of deterministic chaotic behavior. Additionally, chaotic and quasi-periodic behaviors are exhibited for a range of parameter values after adding a perturbation term. The perturbed system's quasi-periodic and chaotic behavior are demonstrated utilizing sensitivity analysis. This is further illustrated through both 2D and 3D graphical representations.