Optical Soliton Analysis for the (3+1)-Dimensional Sakovich Equation in Fluid Dynamics via Generalized Exponential Rational Differential Function Method

We explore optical soliton solutions to the (3+1)-dimensional Sakovich equation, one of the most widely used models in fluid dynamics which accounts for nonlinear wave propagation in multi-dimensional dispersive media. With the majority of studies done on lower-dimensional cases (including but not limited to two-dimensional), systematic analytical solutions for the (3+1)-dimensional variant remain limited, particularly those capturing diverse wave phenomena. To bridge this void, we rely on the generalized exponential rational differential function technique, a solid analytical strategy, which finds solutions between rational forms that integrate a hyperbolic and trigonometric form. Utilizing this technique with traveling wave transformations in a systematic manner, we accomplish multiple families of exact optical soliton solutions with different wave structures. The solutions obtained are compared quantitatively, demonstrated by rich 2D contours and 3D surface visualizations at various parameter ranges, highlighting the dynamical behavior of the system. The analytical solutions present critical solutions for further exploring the properties of wave behaviors in plasma physics, shallow water waves, optical fiber communications and nonlinear dispersive systems. The novel aspect of this work is that systematic generation of different solution families for the (3+1)-dimensional Sakovich equation is established using a powerful approach not used previously for this model, thus broadening the analytical toolbox for multidimensional nonlinear evolution equations and providing the core building blocks for further development of complex wave processes in fluid dynamics and nonlinear optics.