Higher Order Modulation Equations for a Boussinesq Equation

Details Higher Order Modulation Equations for a Boussinesq Equation Higher Order Modulation Equations for a Boussinesq Equation

2002-07-17

arxiv.org/abs/math/0207148v1

Mathematics

Analysis of PDEs

Scientific paper

10.1137/S1111111102411298

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.

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