Explanation of Instabilities Observed on a Fermi-Pasta-Ulam Lattice

Abstract
Exponential instability of waves on the cubically nonlinear, one-dimensional lattice is considered. The lattice has been modeled by the modified Korteweg-de Vries (mKdV) equation. It is shown that some solutions of the mKdV equation are unstable, and that these mKdV instabilities correspond to the instabilities observed on the lattice. Such instabilities may be important in determining whether or not a system behaves stochastically.