We study Klein-Gordon chains with attractive nearest neighbour forces and
convex on-site potential, and show that there exists a two-parameter family of
periodic travelling waves (wave trains) with unimodal and even profile
functions. Our existence proof is based on a saddle-point problem with
constraints and exploits the invariance properties of an improvement operator.
Finally, we discuss the numerical computation of wave trains.Comment: 12 pages, 3 figure