Exponential localization of odd, even, and multi-pulse discrete breathers in Fermi–Pasta–Ulam–Tsingou lattices

Discrete breathers are spatially localized periodic solutions in nonlinear lattices. The existence of odd and even symmetric single-pulse and multi-pulse discrete breathers has been proved in the one-dimensional Fermi–Pasta–Ulam–Tsingou lattices with even interaction potentials [Yoshimura and Doi, J. Differ. Equations 298, 560–608 (2021)]. We prove that those discrete breathers are exponentially localized in space.