A modified discrete sine-Gordon Model

We modify the recently proposed model of Speight and Ward to make it possess time dependent solutions. We find that for each lattice spacing and for each velocity of the sine Gordon kink we can find a modification of the model for which this kink is a solution. We find that this model has really 3 ``kink-like" solutions; the original kink, the static kink and a further kink moving with velocity $v\sim0.97$. We discuss various properties of the model, from the point of view of its usefulness for numerical simulations.