Alexandria Engineering Journal (Dec 2024)
Pfaffian solutions and nonlinear dynamics of surface waves in two horizontal and one vertical directions with dispersion, dissipation and nonlinearity effects
Abstract
This study delves into the exploration of the (3+1)-dimensional generalized nonlinear fractional Konopelchenko–Dubrovsky–Kaup–Kupershmidt (GFKDKK) system, a crucial nonlinear evolution equation governing wave motion across various physical domains. The core aim is to devise innovative analytical solutions for this system employing the Khater III technique and an enhanced Kudryashov methodology integrated with the conformable fractional derivative.The GFKDKK system holds pivotal significance in modeling and comprehending diverse scientific phenomena, ranging from fluid dynamics to plasma physics and nonlinear optics. This research endeavors to harness the potential of the Khater III technique and the updated Kudryashov approach to offer fresh analytical insights into nonlinear fractional differential equations, thus enriching the existing knowledge base in this domain.The attained solutions furnish invaluable insights into the dynamics of the system and its potential applications, thereby facilitating the development of effective numerical simulations and analytical frameworks. The study’s significance lies in its contribution to the ongoing exploration of nonlinear fractional differential equations and their practical implications across various industries.In conclusion, the research affirms the efficacy of the Khater III method and the enhanced Kudryashov technique, complemented by the conformable fractional derivative, in obtaining analytical solutions for the (3+1)-dimensional GFKDKK system. The novelty lies in the application of these methodologies to this specific system, resulting in the discovery of new analytical solutions that enhance our understanding of its behavior and characteristics.
