Qualitative analysis and explicit solutions of perturbed Chen–Lee–Liu equation with refractive index

The main purpose of this article is to study the qualitative analysis and explicit solutions of perturbed Chen-Lee-Liu equation with refractive index. By utilizing wave transformation, two-dimensional dynamics in a plane are obtained. Using the qualitative theory of planar dynamical systems, a series of planar phase portraits are presented. By analyzing the bifurcations of these phase portraits and the characteristics of equilibrium points, some explicit solutions such as Jacobian function solutions and hyperbolic function solutions are constructed. These can further understand the dynamic behavior of perturbed Chen-Lee-Liu equation and their wave propagation.