Type: Article
Publication Date: 2018-01-01
Citations: 5
DOI: https://doi.org/10.1137/17m1162184
We investigate the long time behavior of waves in crystals. Starting from a linear wave equation on a discrete lattice with periodicity $\varepsilon>0$, we derive the continuum limit equation for time scales of order $\varepsilon^{-2}$. The effective equation is a weakly dispersive wave equation of fourth order. Initial values with bounded support result in ring-like solutions, and we characterize the dispersive long time behavior of the radial profiles with a linearized KdV equation of third order.