{
  "abstract": "We construct a family of self-dual $(1+1)$-dimensional $\\mathbb{CP}^1$ sigma models whose potentials $V$ are determined from pre-potentials $U$ by Platonic geometry. Using the round metric on $\\mathbb{S}^2\\simeq\\mathbb{CP}^1$ and the generalized self-duality formalism, we build symmetry-invariant pre-potentials $U$ from the unit vertices of each Platonic solid intersecting the unit circumsphere. The regular-lattice sites associated with vertex, face-center, and edge-midpoint directions are critical points of $U$ and degenerate vacua of the scalar potential $V$. Dual solids share the same regular lattice but generate different pre-potentials, charges, potentials, and metric-gradient flows. Numerical integration reveals distinct self-dual trajectories and energy-density profiles, including multi-peak structures for paths passing near saddle points, while solutions with the same endpoint difference $ΔU$ have the same total energy. The positive maxima of $V$ are also organized into symmetry orbits. This construction provides a geometric prescription for controlling the vacuum structure and self-dual sectors of $\\mathbb{CP}^1$ models with a potential.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12385",
  "author_total": 2,
  "authors": [
    {
      "name": "L. A. Ferreira"
    },
    {
      "name": "G. Marcelino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpxwtaq6srp8v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12385",
  "fulltext_url": null,
  "id": "bpxwtaq6srp8v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12385",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7221077315",
  "pdf_url": "https://arxiv.org/pdf/2610.12385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpxwtaq6srp8v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12385"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Platonic self-dual solitons in a (1+1)-dimensional $\\mathbb{CP}^1$ model",
  "title_text": "Platonic self-dual solitons in a (1+1)-dimensional ℂℙ^1 model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/bpxwtaq6srp8v",
  "venue": "arXiv",
  "versions": []
}