On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering

• Published in: Indian journal of physics Vol. 93; no. 5; pp. 647 - 656
• Main Authors: Sulaiman, T A, Bulut, H, Yokus, A, Baskonus, H M
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.05.2019; Springer Nature B.V
• Subjects: Astrophysics and Astroparticles; Boussinesq equations; Computational fluid dynamics; Exact solutions; Fluid flow; Norms; Numerical methods; Ocean engineering; Ocean models; Original Paper; Physics; Physics and Astronomy; Shallow water; Stability analysis; Water waves; 02.70.Wz; 02.60.Lj; 03.65.-w; Coupled Boussinesq equation; MEFM; Exact and numerical approximations; Shallow water waves; FDM
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-018-1322-1

The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this study, we investigate the coupled Boussinesq equation which arises in the shallow water waves for two-layered fluid flow. The modified exp ( - φ ( ζ ) ) -expansion function method is utilized in reaching the solutions to this equation such as the topological kink-type soliton and singular soliton solutions. The interesting 2D and 3D graphics of the obtained analytical solutions in this study are presented. Via one of the reported analytical solutions, the finite forward difference method is used in obtaining the approximate numerical and exact solutions to this equation. The Fourier–Von Neumann analysis is used in checking the stability of the used numerical method with the studied model. The L 2 and L ∞ error norms are computed. We finally present a comprehensive conclusion to this study.