Parameter Choices

To reproduce and then go beyond the results of FPU, Fig. 1, and take it to $t = 36,000$, use $N = 32$ and $\alpha = 0.25$. With this choice the energies can be measured every 1000 time steps. A conservative choice of $dt = 0.025$ with 1,000,000 time steps seems to work well. The initial displacement should be proportional to ${\bf u}^{(1)}$, but normalized so the maximum displacement (in the middle) is 1. The initial velocity should be zero. You will find that your initial energy in this mode is considerably smaller than the FPU value. They apparently multiplied all energies (which are in arbitrary units anyway) by 4000 for ease of plotting.