{
  "abstract": "In this work, we analyze the initial boundary value (IBV) problems for the Short Pulse (SP) equation $u_{xt}=u+\\frac{1}{6}(u^3)_{xx}$ (classical solutions) on the half-lines $x\\ge 0$ and $x\\le 0$ under the condition of sufficient decay as $x\\to +\\infty$ or as $x\\to -\\infty$. Using the Riemann--Hilbert (RH) problem approach, we show that these two IBV problems differ substantially regarding the boundary values required for problems to be well-posed. Namely, the solution of the ``right problem'' ($x\\ge 0$) is uniquely determined by the initial data $u(x,0)$, $x\\ge 0$ alone, whereas for the ``left problem'' ($x\\le 0$), two boundary functions $u(0,t)$ and $u_x(0,t)$ have to be prescribed, together with the initial data, for a well-posed problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08105",
  "author_total": 2,
  "authors": [
    {
      "name": "Iryna Karpenko"
    },
    {
      "name": "Dmitry Shepelsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c16nj56b7j4sm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08105",
  "fulltext_url": null,
  "id": "c16nj56b7j4sm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08105",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c16nj56b7j4sm.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08105"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Short Pulse equation on the half lines: a Riemann--Hilbert approach",
  "title_text": "The Short Pulse equation on the half lines: a Riemann--Hilbert approach",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/c16nj56b7j4sm",
  "venue": "arXiv",
  "versions": []
}