Discrete breathers in Fermi-Pasta-Ulam lattices

Abstract

The Fermi-Pasta-Ulam (FPU) paradox was observed fifty years ago. The surprising finding was a localization of energy in the reciprocal q-space of a model with discrete translational invariance, despite the presence of interaction between extended normal modes. Thirty three years later Takeno, Kisoda and Sievers reported on the observation of energy localization in real space for the same class of FPU models, which is as surprising since these excitations, called discrete breathers or intrinsic localized modes, violate the underlying discrete translational symmetry of the model. The past decade has whitnessed a tremendous progress in the theory and applications of discrete breathers, which goes much beyond the scope of the original FPU frame. We use the modern theory of discrete breathers to investigate the properties of these solutions in FPU models, paying special attention to the issues of stability, resonances, wave scattering and energy thresholds.