Existence of exponentially and superexponentially spatially localized breather solutions for nonlinear klein-gordon lattices in ℤd, d ≥ 1

Abstract

We prove the existence of exponentially and superexponentially localized breather solutions for discrete nonlinear Klein-Gordon systems. Our approach considers d-dimensional infinite lattice models with general on-site potentials and interaction potentials being bounded by an arbitrary power law, as well as, systems with purely anharmonic forces, cases which are much less studied particularly in a higherdimensional set-up. The existence problem is formulated in terms of a fixed-point equation considered in weighted sequence spaces, which is solved by means of Schauder's Fixed-Point Theorem. The proofs provide energy bounds for the solutions depending on the lattice parameters and its dimension under physically relevant non-resonance conditions. Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.