In this study, the Lie symmetries of the \((2+1)\) -D Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation, which is considerable extension of the KP equation with applications in water waves, fluid dynamics, nonlinear optics, and mathematical physics were investigated. This study has also focused on the exact solutions of this model. We systematically identify the infinitesimal generators and obtain symmetry reductions that convert the equation into lower-dimensional forms using Lie group analysis. The findings shed information on the solution space of the equation and demonstrate how particular symmetries affect its structure. Moreover, exact solutions describing wave propagation behavior are made possible by the simplified equations. The \(\exp (-\Psi (\omega ))\) -expansion approach yields innovative traveling wave solutions after considerable investigation. Solving the nonlinear evolution equations using this analytical method yields rational, hyperbolic, and trigonometric functions. The research reveals new solutions to the suggested problem using the extremely effective proposed method. The stability of the system is explored by computing stability gains using a linearization technique, revealing solution behavior. 3D, 2D, and contour graphs illustrate the dynamics of the obtained solutions, enhancing our knowledge to suggested problem.
