Analyzing invariants and employing successive reductions for the extended Kadomtsev Petviashvili equation in (3+1) dimensions.

Abstract

In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to the derivation of an optimal system of one-dimensional subalgebras relevant to the equation. This optimal system is utilized to obtain several invariant solutions. The Lie group method is subsequently applied to the reduced governing equations derived from the given equation. We complement our findings with Mathematica simulations illustrating some of the obtained solutions. Furthermore, a direct approach is used to investigate local conservation laws. Importantly, our study addresses a gap in the exploration of the 3D-EXP equation using group theoretic methods, making our findings novel in this context.