Exploring the wave solutions of a nonlinear non-local fractional model for ocean waves
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Source abstract
Abstract
In this research, analytical and semi-analytical soliton solutions for the nonlinear fractional (2 + 1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation (FCBSE) in the non-local form are obtained using recent computational and numerical methods. The FCBSE is a significant model for investigating various phenomena, such as internal ocean waves, tsunamis, river tidal waves, and magneto-sound waves in plasma. The constructed solution helps in understanding the interaction between a long wave moving along the x-axis and a Riemann wave propagating along the y-axis. Various analytical solutions, such as exponential, trigonometric, and hyperbolic, have been formulated differently for this model, which is a specific derivation of the well-known Korteweg–de Vries equation. Density charts in two and three dimensions are used to visualize the behavior of a single soliton in reality through simulations. The results demonstrate the effectiveness of the employed numerical scheme and various methods to ensure the consistency of computational and approximation answers. Overall, this study demonstrates the potential of recent computational and numerical techniques for solving nonlinear mathematical and physical problems.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Nonlinear Waves and Solitons · Mathematical functions and polynomials
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Affiliations
Department of Financial Mathematics, School of Mathematical Sciences, Jiangsu University 1 , Zhenjiang, Jiangsu 212013, People’s Republic of China
Department of Mathematics, College of Science, Taif University 2 , P.O. Box 11099, Taif 21944, Saudi Arabia
School of Medical Informatics and Engineering, Xuzhou Medical University 3 , 209 Tongshan Road, 221004 Xuzhou, Jiangsu Province, People’s Republic of China
Department of Basic Science, Obour High Institute for Engineering and Technology 4 , 11828 Cairo, Egypt
Funding
Natural Science Foundation of China · Natural Science Research of Jiangsu Higher Education Institutions of China · Taif University
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