Solitary wave solutions and stability analysis of notable nonlinear evolution model via two analytical methods

The primary goal of this research is to find solitary wave solutions to the (3 + 1)-dimensional Sakovich equation. The modified F-expansion method and the Sardar sub-equation method are employed to construct solitary wave solutions. Through the applications of modified F-expansion method and Sardar sub-equation method, new and novel soliton-like solutions, trigonometric solutions, rational function solutions, and exponential function solutions have been successfully obtained. In order to visualize their physical behavior, some of these solutions are graphically shown using contour plots, 2D profiles, and 3D surfaces. In addition, the modulation instability of the equation is examined using the linear stability analysis, which offers important information on the stability properties of the obtained wave solutions. This work contributes to a deeper analytical understanding of the Sakovich equation by deriving and analyzing its solitary wave solutions.