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

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 $(\frac{1}{3}{)}^{-}$. As applications, we derive the corresponding Strichartz estimates and establish small-data global well-posedness for the associated nonlinear discrete Klein--Gordon equation.

26 pages