VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

Yingzi Guan, Khaled A. Gepreel and Ji-Huan He
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Yingzi Guan: School of Mathematics and Statistics, Huanghuai University, Zhumadian, P. R. China
Khaled A. Gepreel: ��Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Ji-Huan He: ��National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 03, 1-10

Abstract: Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

Keywords: Trial-Lagrange Function; Euler–Lagrange Equation; Parameterized Variational Principle; Integrability Condition; Special Function (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500543

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