Analytical and numerical simulation of the conformable new extended (2 + 1) dimensional Kadomtsev–Petviashvili equation

Abstract

Partial differential equations are used to model problems in many scientific fields. To solve these equations, analytical and numerical techniques are created. This study considers the conformable version of the expanded Kadomtsev–Petviashvili equation in -dimensions for the first time. New exact and approximative solutions to the equation that do not exist in the literature are obtained using the analytical techniques of the -expansion and modified Kudryashov methods, as well as the numerical technique residual power series method. To better understand the dynamic nature of these findings, we have given 3D, contour, and 2D plots of some of the solutions. The development of numerous new exact solutions has demonstrated the reliability and effectiveness of the methods. We also provide an approximation table of values for the approximate solutions of the given equation using different values for various parameters.