Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers

In this paper, conformable Fokas–Lenells model is under consideration, this model is usually used to simulate the propagation model of femtosecond pulses in single-mode optical fibers. Firstly, the traveling wave transformation is applied to convert the conformable Fokas–Lenells model into two-dimensional planar dynamic system. Secondly, the bifurcation of the dynamics system of the conformable Fokas–Lenells model is discussed by using the theory of the plane dynamics system. What is more, two-dimensional phase portraits, three-dimensional phase portraits and Poincaré sections of the dynamics system with perturbation term are drawn with the help of the Maple mathematical software. Finally, the optical soliton solutions of the conformable Fokas–Lenells model are construct by using the analysis method of planar dynamical system.