A new two-parameter hyperbolic secant distribution through solitary wave solution for the Landau–Ginzburg–Higgs equation

This paper examines the Landau–Ginzburg–Higgs (LGH) equation that arises in mathematical physics. We introduce vital solitary wave solution for the LGH model using the unified solver strategy. We depict the dynamic evolution of the discovered soliton wave. To statistically model the situation, a new two-parameter hyperbolic secant (TPHS) distribution is also derived based on the solution of the nonlinear LGH equation. The unit, generalized, and wrapped two-parameter hyperbolic secants are presented using the TPHS distribution. The probability density function (PDF) plots for each of the models under consideration are shown, demonstrating how adaptable their shapes are to represent various scenarios. Moreover, the hazard rate function (HRF) plots of several considered models are shown.