The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations can be shown for two symmetric solutions.

We show the existence of breather solutions in a nonlinear Klein-Gordon system on a discrete graph with periodic junctions. The proof is based on the Theorem of Crandall-Rabinowitz.

We consider a nonlinear diffusion equation on an infinite periodic metric graph. We prove that the terms which are irrelevant w.r.t. linear diffusion on the real line are irrelevant w.r.t. linear diffusion on the periodic metric graph, too. The proof is based on L1‐L∞ estimates combined with Bloch wave analysis for periodic metric graphs.