{
  "abstract": "We consider the focusing nonlinear fourth-order Schrödinger equation \\begin{equation*} i \\partial_t u + μΔu - Δ^2 u = - |u|^{p-1} u, \\ \\ \\ (t,x) \\in \\mathbb{R} \\times \\mathbb{R}^d, \\end{equation*} where $μ\\ge 0$. The scattering of radial solutions below the ground state is shown by Guo (2016) and Dinh (2021) in the case where $d \\ge 2$ and $1 + 8/d < p < 1 + 8/(d-4)_{+}$. In the present paper, we prove the scattering of non-radial solutions below the ground state in the case where $d \\ge 2$ and $1 + 8/(d-1) \\le p < 1 + 8/(d-4)_{+}$. Our proof is based on the concentration compactness argument by Kenig--Merle (2006). To overcome difficulties in the non-radial case, we use the virial identity in the direction orthogonal to the momentum vector. The condition $p \\ge 1 + 8/(d-1)$ is required to show the positivity of the functional in that virial identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05802",
  "author_total": 3,
  "authors": [
    {
      "name": "Takahisa Inui"
    },
    {
      "name": "Koichi Komada"
    },
    {
      "name": "Kuranosuke Nishimura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab6swc5nfnw3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05802",
  "fulltext_url": null,
  "id": "ab6swc5nfnw3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05802",
  "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": "W7220716055",
  "pdf_url": "https://arxiv.org/pdf/2610.05802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab6swc5nfnw3f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Scattering of non-radial solutions for the fourth-order Schrödinger equation with $\\dot{H}^{1/2}$-critical and supercritical nonlinearity",
  "title_text": "Scattering of non-radial solutions for the fourth-order Schrödinger equation with Ḣ^1/2-critical and supercritical nonlinearity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ab6swc5nfnw3f",
  "venue": "arXiv",
  "versions": []
}