Exact traveling breather solutions in a discrete Klein-Gordon ring

Following an earlier work relating to traveling kinks and pulses in a discrete reaction-diffusion system, we construct exact traveling breather solutions on a closed Klein-Gordon type lattice with a double-well potential at each site. The dynamics consists of a succession of linear regimes and the problem reduces to an appropriate matching for successive regimes. The analysis shows that the so-called marginal modes are not essential for the existence of traveling breathers. Results are shown for a ring with N = 3 sites for the sake of illustration of the principles involved, while a number of basic results are also presented for the open lattice N →, see below.