Novel Exact Traveling Wave Solutions for the (2 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation with Atangana's Space and Time Beta-Derivatives via the Sardar Subequation Method

Annual Meeting in Mathematics 2023

Abstract

The (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation usually describes the interaction of a Riemann wave propagating along the y-axis with a long wave propagating along the x-axis. This equation can also be regarded as a generalization of a Korteweg–de Vries (KdV) equation. In this paper, we generalize the BLMP equation by using Atangana's space and time beta-derivatives. We then use the Sardar subequation method and an appropriate traveling wave transformation to derive exact traveling wave solutions for the (2 + 1)-dimensional BLMP equation with fractional derivatives. The exact solutions of the equation are expressed in terms of generalized trigonometric and hyperbolic functions. These functions, which include both real- and complex-valued functions, are defined in this paper for the first time. Exact solutions are derived for a range of values of fractional orders and 2D, 3D and contour plots of the solutions are shown. Solutions are obtained for a range of parameter values to show some of the types of solution that can occur. As examples, we show solutions with physical behaviors such as a singular bell-shaped solitary wave solution, a solitary wave soliton of kink type and a periodic wave solution. We demonstrate that the proposed technique gives a straightforward and efficient method for deriving new exact traveling wave solutions for nonlinear partial differential equations such as the BLMP equation.