DS solution (absolute value)

 

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 absolute value of the DS solution corresponding to the situation in Low dispersion KP, small data , see 20/2006 for details.

C. Klein, C. Sparber and P. Markowich