Corrections to the KdV approximation for water waves

Details Corrections to the KdV approximation for water waves Corrections to the KdV approximation for water waves

2004-06-21

arxiv.org/abs/math/0406403v2

Mathematics

Analysis of PDEs

50 pages, 6 figures

Scientific paper

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.

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