Continuum limit of fourth-order Schrödinger equations on the lattice

2025/01/20 by Jiawei Cheng, Bobo Hua, Cheng, Jiawei +1
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2501.11661

Abstract

In this paper, we consider the discrete fourth-order Schrödinger equation on the lattice hℤ². Uniform Strichartz estimates are established by analyzing frequency localized oscillatory integrals with the method of stationary phase and applying Littlewood-Paley inequalities. As an application, we obtain the precise rate of L² convergence from the solutions of discrete semilinear equations to those of the corresponding equations on the Euclidean plane ℝ² in the contimuum limit h → 0.

Related

• The fourth-order Schrödinger equation on lattices
• Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit
• Uniform Strichartz estimates on the lattice
• Strichartz estimate for discrete Schrödinger equation on layered King's grid
• Asymptotic behavior of discrete Schrödinger equations on the hexagonal triangulation