Fermi, Pasta, Ulam numerical experiments for a discretized version of the [Korteweg–de Vries equation][1].

>In the Summer of 1953 Fermi, Pasta, Ulam and Mary Tsingou conducted numerical experiments (i.e. computer simulations) of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition would have led them to expect. Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally. Instead, the system exhibited a very complicated quasi-periodic behavior.



  [1]: http://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation