The paper is a strict exploration of the existence, dynamic behavior, and stability of optical soliton states of a (3+1)-dimensional Boussinesq equation system, which is conventionally used to describe fluid mechanics systems but is here applied to the dynamics of waves in nonlinear optical materials. Through the application of two powerful analytic procedures, the expansion method of the \(\phi ^{6}\) -model expansion method and the modified \(exp(-\phi (\varrho ))\) -expansion function method, we have been able to obtain a spectrum of new exact soliton solutions that explain the fine balance between higher-order dispersion and nonlinearity in the multidimensional setting. One of the most important contributions of the given work is the sensitivity analysis of the relevant dynamical system in which the transition between regular soliton behavior and the singular or chaotic one is determined systematically based on the values of the main physical parameters, including stratification and nonlinear gain, which determine the parametric regimes of stable propagation. The results do not merely add to the mathematical physics of the Boussinesq equation, but they provide a new theoretical basis to develop robust high-dimensional optical communications in which interactions between complex spatiotemporal dynamics are common. The physical relevance of the solutions is further confirmed by graphical simulations, which provide a clear picture of the underlying wave phenomena.
