Localised time-periodic solutions of discrete nonlinear Klein-Gordon systems with convex on-site potentials

TL;DR

This paper proves the existence of localized time-periodic solutions in one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials using fixed point theory.

Contribution

It introduces a new fixed point approach to establish the existence of localized solutions in these nonlinear lattice systems.

Findings

Existence of localized solutions is rigorously proven.

The approach employs Schauder's Fixed Point Theorem.

Applicable to general convex on-site potentials.

Abstract

The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a fixed point equation for an operator on some appropriate function space which is solved by means of Schauder's Fixed Point Theorem.