Illustration : Gaussian with phase, epsilon=0.05

Wave breaking in the dispersionless limit of the focusing Nonlinear Schroedinger equation.

The picture on the left depicts the relative amplitude of the corrected solution to the genus-0 solution. The plot is in certain dimensionless variables $\theta,\varkappa$ and the scale is not uniform. The dispersionless parameter is E:= 1e-10.

The scale between the ranges is of order E |ln E| while the scale between peaks in the same range is E.

You can download a large (44Mb) movie showing the picture as we fly around it so as to see it from several angles. (VLC is the best viewer for this, if yours does not work).

Some numerical simulations:

Illustration 1: Gaussian initial data, epsilon=0.09

Illustration 2: Gaussian initial data, epsilon=0.05

Illustration 4: Gaussian with phase, epsilon=0.03