<p>In this paper, we study the dynamic behaviors of a high order nonlinear partial differential equation, known as eight-order (3+1)-dimensional Kac–Wakimoto equation. The proposed model have a wide range of applications in physics and nonlinear science. Furthermore, the suggested model is advantageous for the investigation of wave turbulence in fluids, which involves the transfer of energy across a variety of wave numbers. This phenomena is recognized in oceanographic research that involves internal waves and the sea surface, where complex multi-dimensional interactions are essential. By employing the complex wave transformation, we derive the nonlinear ordinary differential equation of the governing model. Advanced analytical methods are employed for developing a variety of soliton solutions, such as mixed, dark, bright-dark, bright, and combined solitons. The analytical techniques applied are known as, the modified F-expansion method, the modified generalized exponential rational function method, and the multivariate generalized exponential rational integral function method, to extract a wide range of soliton solutions for the proposed model. The results demonstrate the adaptability of the techniques used and their success in solving difficult nonlinear partial differential equations. The soliton solutions of the system are analyzed using a wide range of physical parameter sets and values. In order to elucidate the behavior of solutions for various types of parameter values, a variety of graph types are incorporated. The findings reveal the flexibility of the used methods and their efficiency in solving complex nonlinear partial differential equations.</p>