English

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}
}