Bright and dark breathers in Fermi-Pasta-Ulam lattices

Abstract

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional $\mathrm{FPU}$ lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, C. R. Acad. Sci., Ser. I: Math, 332, 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers nonpredicted in the above cited reference. In particular, for a class of asymmetric $\mathrm{FPU}$ potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.