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.

中文翻译：

---

新颖的孤子结构和耦合希格斯场方程的动力学行为

在本文中，我们考虑耦合希格斯场方程，它解释了守恒标量核子与中性标量介子相互作用的结构。我们使用雅可比椭圆函数 (JEF) 技术获得模型的周期和冲击波剖面。结果采用三角函数、双曲函数和有理函数解的形式。从多个角度研究同一模型的动力学行为，包括分岔、准周期运动、混沌模式、Lyapunov 指数和敏感性分析。