Higher Order Modulation Equations for a Boussinesq Equation

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.

Locations

• SIAM Journal on Applied Dynamical Systems - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View