TY - JOUR
AU - Pleumpreedaporn, Chanidaporn
AU - Pleumpreedaporn, Songkran
AU - Moore, Elvin J.
AU - Sirisubtawee, Sekson
AU - Sungnul, Surattana
PY - 2024/03/31
Y2 - 2024/06/24
TI - 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
JF - Thai Journal of Mathematics
JA - Thai J Math
VL - 22
IS - 1
SE - Articles
DO -
UR - https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1595
SP - 1–18
AB - <p>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.</p>
ER -