{
  "abstract": "In this paper, we propose an integrable semi-discretization of the two-component Hunter--Saxton (2-HS) equation, the short-wave limit of the two-component Camassa--Holm (2-CH) equation. At the continuous level, we show that the 2-HS equation can be derived from a new bilinear formulation, distinct from the conventional one in the literature, via a pseudo 2-reduction and a hodograph transformation. For the semi-discrete construction, we first discretize the underlying bilinear equations in the spatial direction. We then impose the pseudo 2-reduction and apply a discrete hodograph transformation to obtain the semi-discrete system in the physical variables. To the best of our knowledge, the resulting system is the first integrable semi-discretization that preserves the two-component structure of the 2-HS equation. We construct the N-soliton solutions of the continuous and semi-discrete systems in Wronskian and Casoratian forms, respectively. The integrability of the semi-discrete system is inherited from the underlying integrable hierarchy and is further verified by a Lax pair.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18701",
  "author_total": 4,
  "authors": [
    {
      "name": "Ayako Hori"
    },
    {
      "name": "Yuta Tanaka"
    },
    {
      "name": "Ken-ichi Maruno"
    },
    {
      "name": "Yasuhiro Ohta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d07c9ck0r6mkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18701",
  "fulltext_url": null,
  "id": "d07c9ck0r6mkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18701",
  "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",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7165147368",
  "pdf_url": "https://arxiv.org/pdf/2606.18701",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d07c9ck0r6mkb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2606.18701",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18701"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "An integrable semi-discretization of the two-component Hunter-Saxton equation",
  "title_text": "An integrable semi-discretization of the two-component Hunter-Saxton equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/d07c9ck0r6mkb",
  "venue": "arXiv",
  "versions": []
}