{
  "annotation_id": "0f3cc963-4347-4e5c-b477-9b2b7b25cb4a",
  "date_created": "2026-03-02T18:01:49.226000Z",
  "date_modified": "2026-03-02T18:01:49.226000Z",
  "file_hash": "6573df04afe64c19e1840a3e6f74b47e19472728e74aa387035e5a3f3fe6ee06",
  "private": false,
  "record": {
    "abstract": "We introduce a new, more general type of nonlinear gauge transformation in\nnonrelativistic quantum mechanics that involves derivatives of the wave\nfunction and belongs to the class of B\\\"acklund transformations. These\ntransformations satisfy certain reasonable, previously proposed requirements\nfor gauge transformations. Their application to the Schr\\\"odinger equation\nresults in higher order partial differential equations. As an example, we\nderive a general family of 6th-order nonlinear Schr\\\"odinger equations, closed\nunder our nonlinear gauge group. We also introduce a new gauge invariant\ncurrent ${\\bf \\sigma}=\\rho {\\bf \\nabla}\\triangle \\ln \\rho $, where\n$\\rho=\\bar\\psi \\psi$. We derive gauge invariant quantities, and characterize\nthe subclass of the 6th-order equations that is gauge equivalent to the free\nSchr\\\"odinger equation. We relate our development to nonlinear equations\nstudied by Doebner and Goldin, and by Puszkarz.",
    "arxiv_id": "quant-ph/0201004",
    "authors": [
      "Gerald A. Goldin",
      "Vladimir M. Shtelen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1465514",
    "title": "On gauge transformations of B\\\"acklund type and higher order nonlinear   Schr\\\"odinger equations",
    "url": "https://arxiv.org/abs/quant-ph/0201004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0df58a23-1d79-409c-a1f7-1af333f85907",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}