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An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation
Abstract
In this paper, we propose an explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation on the one-dimensional torus 𝕋. By carefully designing numerical approximations for the integrals in Fourier space, we construct a third-order scheme and provide a rigorous global error analysis. More precisely, we prove that the scheme achieves third-order convergence in Hr(𝕋) for the initial data in Hr+4(𝕋) with r>1/2. Furthermore, the third-order convergence in L2(𝕋) is established for the initial data in H4(𝕋). Numerical experiments are presented to confirm the theoretical convergence results.
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BibTeX
@misc{luo2026explicit,
title = {{An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation}},
author = {Shengxin Luo and Bin Wang and Yan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34918},
eprint = {2610.34918},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34918},
}
RIS
TY - UNPB
TI - An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation
AU - Shengxin Luo
AU - Bin Wang
AU - Yan Wang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34918
UR - https://arxiv.org/abs/2610.34918
AB - In this paper, we propose an explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation on the one-dimensional torus 𝕋. By carefully designing numerical approximations for the integrals in Fourier space, we construct a third-order scheme and provide a rigorous global error analysis. More precisely, we prove that the scheme achieves third-order convergence in H^r(𝕋) for the initial data in H^r+4(𝕋) with r>1/2. Furthermore, the third-order convergence in L^2(𝕋) is established for the initial data in H^4(𝕋). Numerical experiments are presented to confirm the theoretical convergence results.
ER -