{
  "abstract": "We consider the asymptotic behavior of solutions to inhomogeneous nonlinear Schrödinger equations with non-gauge-invariant nonlinearities. The spatial coefficient in the nonlinear term may have different orders of singularity at the origin and decay at infinity. Under a coercivity condition involving the coefficient and the nonlinearity, we show that no scattering states exist for the equation below a Strauss-type threshold determined by the decay at infinity. Our class includes nonlinearities with a dominant non-oscillatory component. We also prove a complementary small-data scattering result above this threshold, using non-admissible Strichartz estimates in Lorentz spaces adapted to the singular coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06404",
  "author_total": 3,
  "authors": [
    {
      "name": "Mourad Grira"
    },
    {
      "name": "Hayato Miyazaki"
    },
    {
      "name": "Slim Tayachi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exrn2gqgzew0z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06404",
  "fulltext_url": null,
  "id": "exrn2gqgzew0z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06404",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212020206",
  "pdf_url": "https://arxiv.org/pdf/2609.06404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exrn2gqgzew0z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance",
  "title_text": "Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/exrn2gqgzew0z",
  "venue": "arXiv",
  "versions": []
}