Kink dynamics in a novel discrete sine-Gordon system

A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which saturates this bound. There is no Peierls potential barrier, and consequently the motion of a kink is simpler, especially at low speeds. At higher speeds, it radiates and slows down. AMS Classification numbers 58F, 70F. 1 Introduction There are many nonlinear systems, in one spatial dimension, which admit topologically-stable kink solutions: for example, the sine-Gordon and phi-four systems. They have many physical applications. For applications in, say, condensed-matter physics or biophysics, an accurate model should take the discreteness of space into account --- in other words, the kinks live on a one-dimensional lattice rather than in a continuum. A discrete version of the sine-Gordon system which has been extensively studied is the Frenkel-Kontorova model, in which the partial derivative @=@x of..