Title: Symmetry analysis of the (3+1) dimensional Kadomtsev-Petviashvili equation with variable coefficients and an arbitrary nonlinear term

Authors: Preeti Devi; K. Singh

Addresses: Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, HP, India ' Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, HP, India

Abstract: In this research, the (3+1) dimensional Kadomtsev-Petviashvili (KP) equation with time-dependent variable coefficients and an arbitrary nonlinear term has been investigated by using the classical Lie symmetry approach. A number of governing equations have been worked out to obtain the admissible forms of the arbitrary variable coefficients, in general. To illustrate further the reductions and extraction of the exact solutions, the variable coefficients have been taken, in particular, as power functions of 't'. The dimensional reductions of the KP equation have been shown in a systematic manner, leading eventually to nonlinear ordinary differential equations (ODEs). The solutions to these nonlinear ODEs have been furnished, wherever non-trivial Lie symmetries were admitted, and derivation of the exact solution was possible.

Keywords: nonlinear partial differential equation; (3+1) dimensional KP equation; Lie symmetry; group generators; exact solutions.

DOI: 10.1504/IJDSDE.2023.129512

International Journal of Dynamical Systems and Differential Equations, 2023 Vol.13 No.1, pp.1 - 21

Received: 30 Dec 2020
Accepted: 21 Jan 2022
Published online: 13 Mar 2023 *

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