Computational and numerical simulations; the generalized (2+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation

Abstract

This study discusses several analytical and approximate solutions to the generalized Camassa–Holm– Kadomtsev–Petviashvili (CHKP) problem in (2+1) dimensions, which have been recently discovered. The model describes the interesting shapes that liquid droplets can take due to dispersion. The process involves the movement of molecules in a liquid and the movement of particles caused by evaporation. Colloidal particles develop unique cracking patterns when a deposit dries up. A novel approach to solving solitary waves is presented, which combines the Khater II approach with generalized rationalization and Adomian decomposition. To demonstrate the contribution of this paper, several graphical representations, including two-dimensional, three-dimensional, and density plots, are used. The results are compared with previously published works. The methods presented in this study are effective, convenient, and easy to use in solving a range of partial differential equations that are nonlinear in nature. The use of these methods enables the accurate and efficient analysis of the behavior of the CHKP model, providing insights into the formation of interesting shapes of liquid droplets due to dispersion. The comprehensive analysis of the results using various graphical representations and comparison with previous studies enhances the scientific significance of the research.