{
  "abstract": "In this paper, we continue the study of Himonas and Yan\\cite{himonas2024schrodinger,himonas2026higher,himonas2024higher} on the nonlinear Schrödinger equation with a dispersion of order $2m$ and cubic nonlinearities, \\[ iu_t+\\left( -1 \\right) ^{m+1}\\partial _{x}^{2m}u=N_k\\left( u,u,u \\right), \\] where, $m\\ge1$ being an integer, \\[N_0\\left( u,u,u \\right) =uuu,\\quad N_1\\left( u,u,u \\right) =\\bar{u}uu,\\quad N_2\\left( u,u,u \\right) =\\bar{u}\\bar{u}u,\\quad N_3\\left( u,u,u \\right) =\\bar{u}\\bar{u}\\bar{u},\\] We derive trilinear estimates at lower regularity and thereby prove that the cNLS-2m on the half-line is well-posed at the optimal regularity $s=-\\fr{m-1}{2}$. This improves the previous result, $s>-\\fr{m-1}{2}$, and answers an open question left in \\cite{himonas2026higher}. In addition, for $k=0,2$, we establish well-posedness at $s=-\\fr{m-1}{2}$ as well. Moreover, for $k=3$, the nonlinearity exhibits a stronger resonance relation, which implies well-posedness for $s>-\\fr{2m-1}{3}$. Our derivation of the trilinear estimates relies on varieties of Strichartz estimates, which differs from the $[k;Z]$-multiplier norm method employed in \\cite{himonas2026higher}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02747",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuhao Xi"
    },
    {
      "name": "Shenghao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6t34ztt2jsr58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02747",
  "fulltext_url": null,
  "id": "6t34ztt2jsr58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02747",
  "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": "W7220378480",
  "pdf_url": "https://arxiv.org/pdf/2610.02747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t34ztt2jsr58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lower regularity well-posedness for a higher-order Schrödinger equation with cubic nonlinearities on the half-line",
  "title_text": "Lower regularity well-posedness for a higher-order Schrödinger equation with cubic nonlinearities on the half-line",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/6t34ztt2jsr58",
  "venue": "arXiv",
  "versions": []
}