Solitary waves on nonlocal Fermi–Pasta–Ulam lattices: Exponential localization

The paper is devoted to Fermi–Pasta–Ulam lattices with nonlocal interaction. Under natural assumptions we show that all solitary traveling waves are exponentially localized. We reduce the problem to a linear eigenvalue problem for certain integral operator. Then we use functional analysis tools and exponentially weighted spaces of functions to prove the localization of solitary waves.