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Existence of exponentially and superexponentially spatially localized breather solutions for nonlinear klein–gordon lattices in ℤd, d ≥ 1
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 2 / May 2022
- Published online by Cambridge University Press:
- 16 June 2022, pp. 480-499
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- Article
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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 higher-dimensional 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.
