Various Solitary Wave form Solutions and Conserved Vectors of the (2+1)-Dimensional Generalized Benjamin-Ono Equation in Fluid Mechanics

Abstract In this study, we investigate the (2+1)-dimensional generalized Benjamin-Ono equation, a model relevant in fluid dynamics, nonlinear optics, and plasma physics. Our primary aim is to analyse the equation using Lie group theory and derive exact solutions that capture its dynamic behaviours. We first determine the Lie point symmetries of the equation and compute their commutator and adjoint representations. Using these symmetries, we perform reductions that facilitate the construction of closed-form solutions via different ansatz methods. These yield solutions expressed in diverse functional forms such as Jacobi elliptic, hyperbolic, rational, exponential, and trigonometric functions, which are central to nonlinear science and engineering applications. To aid interpretation, we present visual analyses of the solutions via 3D, 2D, and density plots. With appropriate parameter choices, these graphs illustrate wave behaviours. Finally, conserved vectors of the model are derived using Ibragimov’s theorem, offering insight into the system’s underlying conservation laws.