Small dispersion KdV, hump-like data

 
In the small dispersion limit ( ε << 1), KdV solutions develop a zone of rapid modulated oscillations near shocks of the dispersionless equation, the Hopf equation. The video shows the solution for  ε = 0.01 for the initial data -sech^2(x). The video of the detailed oscillatory zone for this case can be found at Low-dispersion KdV (zoom). See 99/2005 for details and references.
T. Grava and C. KleinSmall-dispersion_KdV_%28zoom%29.htmlhttp://www.mis.mpg.de/preprints/2005/prepr2005_99.htmlshapeimage_1_link_0shapeimage_1_link_1