The coupled-Higgs equation, which depicts a system of preserved scalar nucleons cooperating with unbiased scalar mesons, is investigated using the $ϕ^{6}$ $ϕ^{6}$ -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 $m \to 0$ $m \to 0$ and $m \to 1$ $m \to 1$ 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.

Keywords:

PACS: 02.30.Jr, 02.30.Hq, 02.30.Rz, 02.90.+p, 02.70.-c

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