Novel soliton structures and dynamical behaviour of coupled Higgs field equations

In this paper, we consider the coupled Higgs field equations, which explain the structure of the conserved scalar nucleons interacting with a neutral scalar meson. We obtain periodic and shock-wave profiles of the model using the Jacobi elliptic function (JEF) technique. The outcomes are in the form of trigonometric, hyperbolic, and rational function solutions. The dynamical behavior of the same model is investigated from several viewpoints, including bifurcation, quasi-periodic motion, chaotic patterns, Lyapunov exponents, and sensitivity analysis.