Dynamics of chains with non-monotone stress-strain relations. II. Nonlinear waves and waves of phase transition

We investigate the dynamics of a one dimensional mass-spring chain with non-monotone dependence of the spring force vs. spring elongation. For this strongly nonlinear system we find a family of exact solutions that represent nonlinear waves. We have found numerically that this system displays a dynamical phase transition from the stationary phase (when all masses are at rest) to the twinkling phase (when the masses oscillate in a wave motion). This transition has two fronts which propagate with different speeds. We study this phase transition analytically and derive relations between its quantitative characteristics.