Computational analysis and wave dynamics of the (2+1)-dimensional Pavlov equation via semi-analytical schemes

Abstract

This study explores the wave dynamics of the (2 + 1)-dimensional Pavlov equation, a significant model in differential geometry and fluid dynamics, using two powerful semi-analytical methods: the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). A rigorous mathematical foundation is provided through convergence analysis based on the Banach fixed-point theorem. Methodologically, while both schemes effectively capture the stable propagation of kink-type solitary waves, they follow distinct algorithmic pathways. HPM operates directly through homotopy parameter expansions without spatial integration constraints, whereas ADM involves inverse spatial operators that inherently require careful treatment of integration constants. We demonstrate that when identical boundary conditions ( u _n (0, y , t ) = 0) are strictly imposed on the spatial integration constants in ADM, both semi-analytical approaches converge to structurally comparable series terms. Numerical evaluations within the valid radius of convergence ( t = 0.01 and t = 0.05) reveal that ADM consistently achieves approximately twice the accuracy of HPM, with absolute errors roughly half those of HPM across the tested spatial domain, while both schemes retain rapid convergence to the exact solution.