{
  "abstract": "In this paper, we consider the orbital stability of solitary waves for the derivative nonlinear Schrödinger equation $$iq_t+q_{xx}+i\\partial_x\\bigl(|q|^2q\\bigr)=0, \\quad (t,x)\\in\\mathbb{R}\\times\\mathbb{R}.$$ For the endpoint solitary waves satisfying $c>0$ and $c^2=4ω$, we prove the orbital stability in $H^1(\\mathbb{R})$ without any additional assumptions. The proof uses conservation of mass and the second Hamiltonian $\\mathcal{H}_2$ to keep the Bäcklund-transformed solution small in $H^1(\\mathbb{R})$ uniformly in time. We establish an inverse Bäcklund compactness result to reconstruct the algebraic solitary wave as the spectral zero approaches the negative real axis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15507",
  "author_total": 3,
  "authors": [
    {
      "name": "Jia Shen"
    },
    {
      "name": "Yifei Wu"
    },
    {
      "name": "Changping Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czc7tyffktdar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15507",
  "fulltext_url": null,
  "id": "czc7tyffktdar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15507",
  "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": "W7221777869",
  "pdf_url": "https://arxiv.org/pdf/2610.15507",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czc7tyffktdar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15507",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15507"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case",
  "title_text": "Orbital stability of solitary wave solutions of the derivative nonlinear Schrödinger equation in the endpoint case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/czc7tyffktdar",
  "venue": "arXiv",
  "versions": []
}