Dispersive estimates for discrete Klein-Gordon equations on one-dimensional lattice with quasi-periodic potentials

TL;DR

This paper establishes dispersive decay estimates for the discrete Klein-Gordon equation with quasi-periodic potentials on a one-dimensional lattice, leading to Strichartz estimates and global well-posedness results.

Contribution

It proves dispersive estimates for the discrete Klein-Gordon equation with quasi-periodic potentials, extending understanding of decay rates and nonlinear dynamics.

Findings

Dispersive decay rate persists as (1/3)^- for small potentials.

Derived Strichartz estimates for the linear equation.

Established small-data global well-posedness for the nonlinear equation.

Abstract

We prove $\ell^{1}\!\to\!\ell^{\infty}$ dispersive estimates for the discrete Klein--Gordon equation on $\mathbb Z$ with small real-analytic quasi-periodic potentials, showing that the time-decay rate persists as $(\tfrac13)^{-}$. As applications, we derive the corresponding Strichartz estimates and establish small-data global well-posedness for the associated nonlinear discrete Klein--Gordon equation.