Stability, sensitivity, chaotic behavior, and soliton solution of the perturbed Kaup-Newell equation

The main topic of this paper is to examine the dynamical behavior and soliton solutions of the perturbed Kaup–Newell equation. We employ the Jacobi elliptic function (JEF) method to determine the soliton solution of the model. We use tools like phase portraits, Hamiltonian systems, Poincaré maps, Lyapunov exponents, sensitivity analysis, and bifurcation diagrams to investigate the chaotic behavior of the model discussed in this paper. The analysis presented here is crucial for making decisions to achieve better control, optimization, and overall system improvement.