Difference KdV-asymptotic solution

 

The video shows the difference between the KdV solution and the corresponding asymptotic solution in KdV + asymptotic solution (Whitham). The oscillatory zone is shown in red. It can be seen that the approximation is worst near breakup and at the boundary of the oscillatory zone. There are always KdV oscillations outside the oscillatory zone, see 99/2005 for details and references.

T. Grava and C. Klein