Existence and Stability of Odd and Even Parity Discrete Breathers in Fermi--Pasta--Ulam Lattices

Abstract

Discrete breathers are spatially localized periodic solutions in nonlinear lattices. We prove the existence of odd and even parity discrete breathers, i.e., Sievers--Takeno and Page modes, in one-dimensional Fermi--Pasta--Ulam lattices with periodic boundary conditions. Moreover, we prove that the Sievers--Takeno mode is spectrally unstable, while the Page mode is spectrally stable.