Analysis and computation of travelling wave solutions of bistable differential-difference equations

We consider travelling wave solutions of a class of differential-difference equations. Our interest is in understanding propagation failure, the directional dependence due to the discrete Laplacian, and the relationship between travelling wave solutions of the spatially continuous and spatially discrete limits of this equation. The differential-difference equations that we study include damped and undamped nonlinear wave and reaction-diffusion equations as well as their spatially discrete counterparts. Both analytical and numerical results are given.