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arXiv · 2603.20627

On Optimal Convergence Rates for the Nonlinear Schr\"{o}dinger Equation with a Wave Operator via Localized Orthogonal Decomposition

Hanzhang Hu·Zetao Ma·Lei Zhang
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Abstract

In this paper, we develop a Localized Orthogonal Decomposition (LOD) method for the two-dimensional time-dependent nonlinear Schr\"{o}dinger equation with a wave operator. We prove that our method preserves conservation laws and admits a unique numerical solution; furthermore, we obtain unconditional (i.e., time-step restriction-free) optimal-order superconvergent \(L^p\) error estimates. To complement the theoretical analysis, we present a series of numerical simulations that verify the analytical results and further illustrate structural aspects of the problem.

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Hanzhang Hu, Zetao Ma, Lei Zhang. 2026-03-21. On Optimal Convergence Rates for the Nonlinear Schr\"{o}dinger Equation with a Wave Operator via Localized Orthogonal Decomposition. https://arxiv.org/abs/2603.20627

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