Exact Solutions for the Generalized Atangana-Baleanu-Riemann Fractional (3 + 1)-Dimensional Kadomtsev–Petviashvili Equation

Abstract

In this article, the generalized Jacobi elliptic function expansion method with four new Jacobi elliptic functions was used to the generalized fractional (3 + 1)-dimensional Kadomtsev–Petviashvili (GFKP) equation with the Atangana-Baleanu-Riemann fractional derivative, and abundant new types of analytical solutions to the GFKP were obtained. It is well known that there is a tight connection between symmetry and travelling wave solutions. Most of the existing techniques to handle the PDEs for finding the exact solitary wave solutions are, in essence, a case of symmetry reduction, including nonclassical symmetry and Lie symmetries etc. Some 3D plots, 2D plots, and contour plots of these solutions were simulated to reveal the inner structure of the equation, which showed that the efficient method is sufficient to seek exact solutions of the nonlinear partial differential models arising in mathematical physics.

Keywords

• fractional (3 + 1)-dimensional Kadomtsev–Petviashvili equation
• Atangana-Baleanu-Riemann fractional derivative
• generalized Jacobi elliptic function expansion method
• bell-shape soliton solution
• exact solutions