Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908574547968000 |
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| author | Li, Hang Li, Xicui Schratz, Katharina Wang, Bin |
| author_facet | Li, Hang Li, Xicui Schratz, Katharina Wang, Bin |
| contents | We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the twisted variable with a dynamically adjusted relaxation parameter that guarantees exact mass conservation. Unlike existing symmetric or structure-preserving low-regularity integrators, which are typically implicit and computationally expensive, the proposed methods are fully explicit, mass-conserving, and well-suited for solutions with low regularity. Furthermore, the schemes can be naturally extended to a broad class of evolution equations exhibiting the structure of strongly continuous contraction semigroups. Numerical results demonstrate the accuracy, robustness, and excellent long-time behavior of the methods under low-regularity conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation Li, Hang Li, Xicui Schratz, Katharina Wang, Bin Numerical Analysis 65M12, 65M15, 65T50, 35Q55 We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the twisted variable with a dynamically adjusted relaxation parameter that guarantees exact mass conservation. Unlike existing symmetric or structure-preserving low-regularity integrators, which are typically implicit and computationally expensive, the proposed methods are fully explicit, mass-conserving, and well-suited for solutions with low regularity. Furthermore, the schemes can be naturally extended to a broad class of evolution equations exhibiting the structure of strongly continuous contraction semigroups. Numerical results demonstrate the accuracy, robustness, and excellent long-time behavior of the methods under low-regularity conditions. |
| title | Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation |
| topic | Numerical Analysis 65M12, 65M15, 65T50, 35Q55 |
| url | https://arxiv.org/abs/2510.02963 |