{
  "abstract": "We study classical soliton solutions in split-signature anti-self-dual Yang-Mills theory. Using Zakharov's dressing method, we construct rational lump solitons, which are localised near two-dimensional surfaces, and wall solitons, which have codimension one. We further describe multi-phase solutions which have multiple walls meeting at trivalent junctions and form four-dimensional foam-like structures. Two-pole solutions describe soliton interactions and we find non-trivial colour-dressed phase shifts for wall interactions. We consider the four-dimensional analogue of Ward's lump scattering for the restricted kinematics of coincident poles and show that there are non-trivial interactions in the collinear limit. Finally, we show that the determinant of the soliton matrix provides a $τ$-function which acts as a potential for gauge-invariant scalar quantities such as the Yang-Mills Lagrangian density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27074",
  "author_total": 1,
  "authors": [
    {
      "name": "Tristan McLoughlin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7263tshyjpfz2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27074",
  "fulltext_url": null,
  "id": "7263tshyjpfz2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27074",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7223088237",
  "pdf_url": "https://arxiv.org/pdf/2610.27074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7263tshyjpfz2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27074"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Classical solitons in anti-self-dual Yang-Mills theory",
  "title_text": "Classical solitons in anti-self-dual Yang-Mills theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/7263tshyjpfz2",
  "venue": "arXiv",
  "versions": []
}