Solitary Wave Propagation in Periodic and Aperiodic Diatomic Toda Lattices

We investigate numerically how a solitary wave propagates in some one-dimensional diatomic periodic and aperiodic Toda lattices. It is found that a nearly stable wave of rather high amplitude can propagate in the periodic lattice. For several of the deterministic aperiodic sequences considered, the damping of the wave in the corresponding lattice is considerable less than for a random lattice. The short range correlation between the atoms in the aperiodic lattices seems to be of main importance for how much the wave is damped. We suggest therefore that the entropy according to Shannon might be a relevant measure for the properties of the lattices in this case. It is shown that this measure yields at least an approximative agreement with what is actually achieved by our numerical experiments. It is also shown that the earlier proposed idea of viewing the process as multiple scattering cannot be applied to other cases than random sequences with small mass-differences.