A model calculation for vibrational propagation in a chain of nonlinear oscillators

We analyze a chain of nonlinear oscillators and calculate transport quantities relevant to the propagation of vibrational excitations in the chain. We obtain explicit expressions for oscillator displacements as well as for the mean-square-displacements of the vibrational excitation for several different initial conditions including a localized and a grating initial condition, and study with their help the effects of nonlinearity on vibrational propagation.