Alexandria Engineering Journal (Jan 2025)
Computational and numerical solutions to the Benney–Luke equation: Insights into nonlinear long wave dynamics in dispersive media
Abstract
The current investigation seeks to explore the nonlinear Benney–Luke model, a governing equation pertinent to the propagation of extended waves within dispersive media, such as those observed in water waves and plasma waves, among other nonlinear wave phenomena. This model is distinguished by its incorporation of both dispersive and nonlinear effects, rendering it a valuable instrument for delving into intricate wave dynamics. Notably, it shares similarities with other prominent nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation and the Boussinesq equation, both of which have been extensively examined within the domain of water waves and associated phenomena.Employing analytical methodologies, specifically the Khater (Khat III) and modified Kudryashov (MKud) methods, the research endeavors to derive exact solutions for the Benney–Luke equation. These solutions serve to elucidate various aspects of long wave behavior in dispersive media, encompassing their propagation characteristics, stability, and potential for inter-wave interactions. Furthermore, a trigonometric-quantic-B-spline (TQBS) scheme is adopted as a numerical approach to corroborate the precision of the derived analytical solutions and demonstrate their relevance across diverse physical scenarios linked to the model under examination.The research outcomes underscore the efficacy of the analytical techniques in generating dependable solutions for the Benney–Luke model. Moreover, through the utilization of the TQBS numerical scheme, the accuracy of the derived analytical solutions is affirmed, thereby ensuring their pragmatic utility across a spectrum of physical scenarios pertinent to the investigated model. This endeavor holds significance in its contribution towards advancing the comprehension of nonlinear wave phenomena within dispersive media, with ramifications spanning multiple disciplines, including fluid dynamics, plasma physics, and nonlinear optics. The novelty of this study lies in its application of the Khater (Khat III) and modified Kudryashov (MKud) methods to the Benney–Luke equation, alongside the integration of the TQBS numerical scheme for solution validation. Positioned within the domain of nonlinear partial differential equations, this research aligns with its broader applications in physics, particularly concerning the investigation of dispersive wave phenomena.
