Discrete Four-Order Schrödinger Equation on the Hexagonal Triangulation

Abstract

In this paper, we establish a decay estimate for the discrete four-order Schrödinger equation on the hexagonal triangulation with γ=0. The proof is based on the uniform estimates of oscillatory integrals, as developed by Karpushkin, along with a key result by Varchenko. Our result is to show the l¹→l^∞ dispersive decay rate is ⟨t⟩^−σ for any 0<σ< 1/2. Additionally, we provide estimates for the inhomogeneous discrete fourth-order Schrödinger equation with γ=0.

Keywords

Schrödinger equation / graph / Strichartz estimate