Mathematical analysis and numerical validation of an extended KdV model for shallow water waves
Abstract
The KdV is one of the most widespread non-linear models, commonly used by coastal engineers, to describe wave propagation in weakly non-linear and weakly dispersive shallow water problems. In this paper, we investigate the solutions of the extended KdV equation, previously formally derived for both the velocity and the free-surface elevation, by analyzing its consistency with the extended Boussinesq equations. Combined with a stability result, this leads to a convergence result. This analysis enables us to derive new linear asymptotic models based on this equation. We then explicitly solve these new linear models and validate the results numerically. Finally, we analyze solitary-wave solutions of the extended KdV model and quantify its improved accuracy.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Coastal and Marine Dynamics
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 33
- Issue
- 0
- Pages
- 467–493
- Publication date
- 29 June 2026
- Language
- EN