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

2025/12/27 by Zhiqiang Wan, Heng Zhang, Wan, Zhiqiang +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2512.22613

openalex publication_date 2025/12/27 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28

Abstract

We prove ℓ¹ → ℓ^∞ 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.

Citations

• Sharp dispersive estimates for the wave equation on the 5-dimensional lattice graph
• The Wave Equation on Lattices and Oscillatory Integrals
• Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices
• The absolutely continuous spectrum of the almost Mathieu operator
• On asymptotic stability of standing waves of discrete Schrödinger equation in \Bbb Z

Related

• On dispersion for Klein Gordon equation with periodic potential in 1D
• Continuum limit of the discrete nonlinear Klein-Gordon equation
• Uniform Strichartz estimates on the lattice
• The Klein-Gordon Equation on \mathbb Z² and the Quantum Harmonic Lattice
• A note on small periodic solutions of discrete nonlinear Klein-Gordon equations