Abstract
The main objective of this work is to study the dynamical behavior and traveling wave solution for the nonlinear Kaup–Newell system in optical fibers. Here, we have constructed periodic wave solutions, kink-shaped solitary solutions and anti-kink solitary solutions through the theory of planar dynamical system. In addition, some other traveling wave solutions of the nonlinear Kaup–Newell system are derived by means of the polynomial complete discriminant system method and symbolic computation, respectively. The trigonometric function solutions, solitary wave solutions, rational function solutions, the hyperbolic function solutions and the Jacobian function solutions are obtained. Finally, 3D-diagram and 2D-diagram of the nonlinear Kaup–Newell system are also plotted.
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