{
  "abstract": "We consider the 1-D focusing cubic NLS with a smooth, spatially-dependent potential which decays rapidly as $x \\rightarrow \\pm \\infty$. As is well known, under sufficient regularity conditions, solutions of the cubic NLS with such a spatially-dependent potential conserve both mass and energy. Additionally, in the absence of a potential, the 1-D focusing cubic NLS admits boosted soliton solutions. Furthermore, in the presence of a potential, the interaction of the potential with boosted soliton solutions to the free case is of active interest in the literature, particularly with respect to the dependence of this soliton-potential interaction on the velocity of the incident soliton. We adapt a finite-difference scheme to the setting of a smooth, rapidly-decaying spatially-dependent potential and show that this adaptation preserves the appropriate mass and energy invariants. Additionally, we use this algorithm to model soliton-potential interactions at a variety of incident soliton velocities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17486",
  "author_total": 2,
  "authors": [
    {
      "name": "Anthony D. Stone Jr."
    },
    {
      "name": "Christopher C. Hogan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnfjd0k3gcrx6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17486",
  "fulltext_url": null,
  "id": "fnfjd0k3gcrx6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17486",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7221770065",
  "pdf_url": "https://arxiv.org/pdf/2610.17486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnfjd0k3gcrx6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Modeling soliton-potential interactions for the 1-D cubic NLS via an invariant-preserving finite-difference method",
  "title_text": "Modeling soliton-potential interactions for the 1-D cubic NLS via an invariant-preserving finite-difference method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/fnfjd0k3gcrx6",
  "venue": "arXiv",
  "versions": []
}