Abstract
•Fractional Chen-Lee-Liu (CLL) equation in optical fibers is studied using beta derivative.•Perturbed and unperturbed cases are discussed.•Fifth-degree nonlinear term describing the evolution of the wave amplitude is considered.•Galilean transformation is used for conversion and the bifurcation behavior is reported.•Sensitive analysis is applied to analyze the quasiperiodic and quasiperiodic-chaotic behaviors.
This paper studies the dynamical behaviors of nonlinear wave solutions of perturbed and unperturbed fractional Chen-Lee-Liu (CLL) equation in optical fibers with a newly defined beta derivative. The coupled amplitude-phase formulation is used for the derivation of a nonlinear differential equation which contains a fifth-degree nonlinear term describing the evolution of the wave amplitude in the nonlinear system. Variety of soliton solutions are found by using the new extended direct algebraic method. Then, discussed model is converted into the planer dynamical system with the help of Galilean transformation and the bifurcation behavior is reported. All possible forms of phase portraits with respect to the parameters of the considered problem are plotted. In addition, by applying an extrinsic periodic force the effect of physical parameters is investigated. Furthermore, sensitive analysis is applied for different initial value problems to analyze the quasiperiodic and quasiperiodic-chaotic behaviors.