Bifurcation Analysis, Chaotic Behavior, Cubic–Quartic Optical Solitons, and Phase Portraits for the Nonlinear Coupled Kaup–Newell Equation in Birefringent Fibers

ABSTRACT The main attention of this paper focuses on studying the dynamical behaviors, cubic–quartic optical solitons, chaotic pattern, and phase portraits for the nonlinear coupled Kaup–Newell equation in birefringent fibers. First of all, by means of traveling wave transforms and homogeneous balance principle, the coupled Kaup–Newell equation in birefringent fibers is simplified into an ordinary differential equation. Secondly, the dynamical properties of two‐dimensional system and the corresponding perturbed system have been studied. Finally, with the assistance of the complete discriminant system method, the optical soliton solutions of the coupled Kaup–Newell equation in birefringent fibers can be derived, which include solitary wave solutions, rational function solutions, Jacobian elliptic function solutions, and hyperbolic function solutions. In addition, two‐dimensional portraits, three‐dimensional portraits, contour plots, density plots, and two‐dimensional gradplots of the obtained solutions are also given by explaining the propagation of optical solitons for the coupled Kaup–Newell equation in birefringent fibers.