Small dispersion KP, small data

 

In the small dispersion limit (ε << 1), KP solutions develop a zone of rapid modulated oscillations near shocks of the dispersionless KP equation. For small initial data of order ε with rapid oscillations in x-direction of order 1/ε, a multi-scales expansion of the KP equation shows that the amplitude of the solution is asymptotically described  by a solution of the Davey-Stewartson equation. The video shows the solution forεε = 0.1 for initial data with compact support, see 20/2006 for details. The corresponding Davey-Stewartson solution can be seen in DS solution (absolute value).

C. Klein, C. Sparber and P. Markowich