Analysis of the Generalized Ostrovsky Equation in the Propagation of Surface and Internal Waves in Rotating Fluids

ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods. This paper investigates the generalized Ostrovsky equation using Lie symmetry group method and low local conservation laws, essential for analyzing differential equations and describing conserved physical and chemical processes. Specific cases reduce it to the Ostrovsky or generalized Korteweg–de Vries (KdV) equations. Detailed calculations of local conservation laws, classical point symmetries, and symmetry reductions are provided, offering invariant solutions and Lie symmetry groups. This research advances the understanding of differential equations and their applications in modeling scientific phenomena.