Travelling breathers in Klein–Gordon chains

We study the existence of travelling breathers in Klein–Gordon chains, which describe nonlinear oscillators linearly coupled in a local anharmonic potential. In this work, we consider a case when the period of the breather and the inverse of the velocity are commensurable. In a neighborhood of critical values of velocity and coupling, we show by a center manifold reduction that the infinite-dimensional problem can be locally reduced to a eight-dimensional reversible differential equation. To cite this article: Y. Sire, G. James, C. R. Acad. Sci. Paris, Ser. I 338 (2004).