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A potential projection method for the nonlinear Schrödinger equation with low regularity potential — arXiv:2610.19430

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19430
License (as archived): CC0-1.0
Archived: 2026-10-15T21:52:26.123Z
SHA-256 of the archived text: 49ce1e908446ec70cc0969fbe7b57acef27452983538fd168ec2e70419e51174
Stable URL of this page: https://metraipolis.com/documento/dc_bbdae3620ef8

How to cite

A potential projection method for the nonlinear Schrödinger equation with low regularity potential — arXiv:2610.19430 — arXiv (en), https://arxiv.org/abs/2610.19430 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bbdae3620ef8 (Metraipolis archive dc_bbdae3620ef8, sha256 49ce1e908446ec70cc0969fbe7b57acef27452983538fd168ec2e70419e51174)

BibTeX

@misc{dcbbdae3620ef8,
  title = {A potential projection method for the nonlinear Schrödinger equation with low regularity potential — arXiv:2610.19430},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19430},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bbdae3620ef8; sha256 49ce1e908446ec70cc0969fbe7b57acef27452983538fd168ec2e70419e51174},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19430. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a potential projection (PP) method for the nonlinear Schrödinger equation (NLSE) with low-regularity and singular potentials by replacing the potential with its Fourier projection (truncated Fourier series). This gives rise to an NLSE with projected potential (NLSEwPP). We rigorously establish its well-posedness under low-regularity potentials, and its convergence to the original NLSE. The NLSEwPP is then directly discretized by the standard time-splitting Fourier pseudospectral (TS-FP) method with the mesh size chosen according to the potential projection parameter, resulting in the fully discrete TS-PP-FP method. Numerically, TS-PP-FP consistently achieves optimal temporal and spatial convergence rates with respect to the regularity of the exact solution under low-regularity and even singular potentials. Compared with the time-splitting Fourier spectral method, TS-PP-FP attains the same convergence rates at significantly lower computational cost and preserves the mass conservation and time symmetry (that are lost in the Fourier spectral discretization of the time-splitting method); compared with the time-splitting FP method, it is substantially more accurate for low-regularity potentials with the same computational cost.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.19430 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T21:36:59.405Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).