Concluding remarks We have investigated the evolution of the initial π-mode for the 1D beam lattice model in comparison with the FPU-β lattice. Consequences obtained so far can be summarised as follows: 1) The growth rate (σ) of the modulational instability increases as the initial amplitude (A0) increases. The critical energy (Ec) for instability decreases as nonlinearity (β) or particle number (N) increases and gives a relation Ec ∝1/βN. 2) Wavenumbers of the modulation found in numerical results are π −Qf but not Qmax. Here Qf is the first growing mode in numerical simulation (Qmax < Qf < π) and Qmax is the maximum growing mode of σ given by the dispersion relation (Eq. (3)) for the modulational instability of the π−mode. 3) The localized energy (Epk) increases as N and A0 increase, and max[Epk] is proportional to the 2 total energy, that is, max[Epk] ∝ NA0. The decay time (td), until then the localization (CB) survives, decreases as A0 increases independent of N, and thus td is found to be dependent on the initial energy 2 density (A0). 4) The localized energy (Epk) tends to a constant as N →∞, while the ratio of localization (RCB) decreases as N →∞, which indicates the existence of the upper limit for the localization (Epk) as N increases.