Higher Order Modulation Equations for a Boussinesq Equation
Analysis of PDEs
2009-11-07 v1 Dynamical Systems
Abstract
In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation alone. We also present the results of numerical experiments which show that the error estimates we derive are essentially optimal.
Cite
@article{arxiv.math/0207148,
title = {Higher Order Modulation Equations for a Boussinesq Equation},
author = {C. Eugene Wayne and J. Douglas Wright},
journal= {arXiv preprint arXiv:math/0207148},
year = {2009}
}