{
  "abstract": "We consider the nonlinear Schrödinger equation on $\\mathbb{R}^{3,1}$, with a class of `mixed' nonlinearities that admit soliton solutions. We are interested in the long-time behaviour of solutions with finite, but possibly large, mass and/or energy. By a spacetime cone, we mean an open set in $\\mathbb{R}^{3,1}_{x,t}$ that is invariant under dilation $(x, t) \\mapsto (αx, αt)$ for all $α> 0$. Our main result is as follows: let $u(x, t)$ be the solution with initial condition in $H^2(\\mathbb{R}^3)$. Let $\\mathscr{M}, \\mathscr{E}$ be the mass and energy of $u$, and let $η= η(\\mathscr{M}, \\mathscr{E}) > 0$ be sufficiently small. Let $C_ε$ be the complement of $N \\geq 1$ of sufficiently thin spacetime cones $\\{ (x, t) \\mid |x-v_jt| \\leq εt \\}$, where $v_1, \\dots, v_N$ are fixed velocities and $ε$ is sufficiently small. If the $L^\\infty$ norm of $u$ in $C_ε$ is $\\leq η$, we prove that $u$ scatters in $C_{2ε} \\subset C_ε$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29265",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew Hassell"
    },
    {
      "name": "Qiuye Jia"
    },
    {
      "name": "Xiaoxu Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33qjym2fd5nj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29265",
  "fulltext_url": null,
  "id": "33qjym2fd5nj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29265",
  "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": "W7223236040",
  "pdf_url": "https://arxiv.org/pdf/2610.29265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33qjym2fd5nj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Scattering in spacetime cones for the nonlinear Schrödinger equation",
  "title_text": "Scattering in spacetime cones for the nonlinear Schrödinger equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/33qjym2fd5nj4",
  "venue": "arXiv",
  "versions": []
}