On Optimal Convergence Rates for the Nonlinear Schrödinger Equation with a Wave Operator via Localized Orthogonal Decomposition
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| Format: | Preprint |
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2026
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| _version_ | 1866911532934234112 |
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| author | Hu, Hanzhang Ma, Zetao Zhang, Lei |
| author_facet | Hu, Hanzhang Ma, Zetao Zhang, Lei |
| contents | In this paper, we develop a Localized Orthogonal Decomposition (LOD) method for the two-dimensional time-dependent nonlinear Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Optimal Convergence Rates for the Nonlinear Schrödinger Equation with a Wave Operator via Localized Orthogonal Decomposition Hu, Hanzhang Ma, Zetao Zhang, Lei Numerical Analysis Computational Physics 35Q55, 65M60, 65M12, 81Q05 In this paper, we develop a Localized Orthogonal Decomposition (LOD) method for the two-dimensional time-dependent nonlinear Schrödinger 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. |
| title | On Optimal Convergence Rates for the Nonlinear Schrödinger Equation with a Wave Operator via Localized Orthogonal Decomposition |
| topic | Numerical Analysis Computational Physics 35Q55, 65M60, 65M12, 81Q05 |
| url | https://arxiv.org/abs/2603.20627 |