Periodic travelling waves in convex Klein-Gordon chains
arXiv:0902.4201 · doi:10.1016/j.na.2009.04.039
Abstract
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.
12 pages, 3 figures