The coupled-Higgs equation, which depicts a system of preserved scalar nucleons cooperating with unbiased scalar mesons, is investigated using the ${\varphi }^6$-model expansion approach in this paper. We want to look at the various particles that are created when scalar nucleons collide with unbiased scalar mesons. The modulus of the elliptic function $m\to 0$ and $m\to 1$ is used to obtain the trigonometric and hyperbolic functions. Under the stated limited constraints, all found solutions are used to validate the partial differential equation. We displayed 3D surfaces and 2D visuals of selected solutions produced with the assistance of a computer program to shed more light on the dynamic behavior of the acquired solutions.

描述了与无偏标量介子合作的保存标量核子系统的耦合希格斯方程，使用${\phi }^{\mathrm{6个}}$-本文中的模型扩展方法。我们想看看标量核子与无偏标量介子碰撞时产生的各种粒子。椭圆函数的模数$米\to 0$和$米\to \mathrm{1个}$用于获得三角函数和双曲函数。在规定的有限约束下，所有找到的解都用于验证偏微分方程。我们展示了在计算机程序的帮助下生成的选定解决方案的 3D 表面和 2D 视觉效果，以更清楚地了解所获得解决方案的动态行为。