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A hyperbolic nonlinear Schrödinger system in multiple spatial dimensions: structure, convergence, and numerical discretization — arXiv:2611.03642

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03642
License (as archived): CC0-1.0
Archived: 2026-11-03T11:36:28.709Z
SHA-256 of the archived text: d24d5a083cc70f981a52fe07413d06688ef94d5476a184f5216169bac7948913
Stable URL of this page: https://metraipolis.com/documento/dc_22ea481bf002

How to cite

A hyperbolic nonlinear Schrödinger system in multiple spatial dimensions: structure, convergence, and numerical discretization — arXiv:2611.03642 — arXiv (en), https://arxiv.org/abs/2611.03642 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_22ea481bf002 (Metraipolis archive dc_22ea481bf002, sha256 d24d5a083cc70f981a52fe07413d06688ef94d5476a184f5216169bac7948913)

BibTeX

@misc{dc22ea481bf002,
  title = {A hyperbolic nonlinear Schrödinger system in multiple spatial dimensions: structure, convergence, and numerical discretization — arXiv:2611.03642},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03642},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_22ea481bf002; sha256 d24d5a083cc70f981a52fe07413d06688ef94d5476a184f5216169bac7948913},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03642. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose and study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation in $N$ spatial dimensions. This is an extension of the recently-proposed 1D hyperbolic NLS model. We study the structure and properties of the hyperbolic approximation and their relation to those of the original system. We show that the N-dimensional hyperbolic system exactly conserves analogs of the mass, energy, and momentum, and that it possesses stationary solutions that are closely related to those of NLS. The hyperbolic system is also shown to admit plane-wave solutions that share some stability properties with those of NLS, and that relaxation can shrink the focusing low-wavenumber modulational instability band as well as introduce a high-wavenumber instability band not present in NLS. We also show that solutions of the hyperbolic system converge to solutions of NLS in the relaxation limit. We present an adaptive-mesh finite volume discretization of the hyperbolic system and demonstrate its effectiveness in handling simulations, including those with geometric obstacles or non-periodic boundary conditions. The effectiveness of the numerical scheme is demonstrated through examples including a Bose-Einstein condensate, line soliton instability, and superflow past a cylinder.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Analysis of PDEs (math.AP) ; Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2611.03642 — 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 2026-11-03T11:05:07.274Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).