2004/06/21 by James Wright, J. Douglas Wright, Wright, J. Douglas
Earth and Planetary Sciences · Engineering · Mathematics · #76B15 #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #Dynamical Systems (math.DS) #FOS: Mathematics #Ocean Waves and Remote Sensing #Wave and Wind Energy Systems #math.AP #math.DS #msc:76B15
paper · pdf · doi:10.48550/arxiv.math/0406403
50 pages, 6 figures
openalex publication_date 2004/06/21 · arxiv created 2004/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to investigate corrections to the common KdV approximation for surface water waves in a canal, we derive modulation equations for the evolution of long wavelength initial data. We work in Lagrangian coordinates. The equations which govern corrections to the KdV approximation consist of linearized and inhomogeneous KdV equations plus an inhomogeneous wave equation. These equations are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation alone.