Damped KdV Equations

We study numerically the long time behavior of a family of weakly damped and forced KdV equation on the Torus. In particular, we point out non trivial dynamics, Sobolev regularization effects.
We also focus on the damping rate for different damping models and introduce a simple function that allows to make a hierarchy between the models. Also, in some cases, we propose a way to rebuild a posteriori the damping operator using samples of the solution.