Dynamical system approach and \(exp(-\Phi (\zeta ))\) Expansion method for optical solitons in the complex nonlinear Fokas–Lenells model of optical fiber

The complex nonlinear Fokas–Lenells (FL) equation to obtain the explicit travelling wave solutions under different values parameters such as solitary wave solutions, kink solitary wave solutions and periodic wave solutions and others solutions are studied using the dynamical system approach. Also, the optical solitons for the FL equation, as well as the plane-wave, complex dark-singular, and complex periodic-singular solutions are obtained via the \(exp(-\Phi (\zeta ))\) $exp(-\mathrm{\Phi }(\zeta ))$ expansion method. In conclusion, graphical representations of these solutions are provided so that the dynamics of these waves can be viewed.