Existence of breathers in nonlinear Klein-Gordon lattices

TL;DR

This paper proves the existence of breathers and time-periodic solutions in nonlinear Klein-Gordon lattices using fixed point theory, advancing understanding of localized oscillations in such systems.

Contribution

It establishes the existence of breathers in nonlinear Klein-Gordon lattices through a fixed point approach, a novel application in this context.

Findings

Existence of breathers proven mathematically.

Application of Schauder's Fixed Point Theorem.

Generalization to infinite lattices.

Abstract

We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder's Fixed Point Theorem.