{
  "abstract": "With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation, as well as the multiple Darboux transformation which allows to obtain compact solutions of this equation. We construct explicitly some solutions for the first orders. Using particular generating functions, we give wronskian representations of the solutions to the sine-Gordon equation. In this case we give different solutions to this equation. We deduce generalized wronskian representations of the solutions to the sine-Gordon equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Pierre Gaillard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ebxzx7fdzqzwx.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "ebxzx7fdzqzwx",
  "issns": [],
  "landing_url": "https://hal.science/hal-05763853v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.nlin"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05763853/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ebxzx7fdzqzwx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05763853",
      "source": "hal",
      "url": "https://hal.science/hal-05763853v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "hal:0.nlin",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Wronskian representations of the solutions to the sine-Gordon equation",
  "title_text": "Wronskian representations of the solutions to the sine-Gordon equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/ebxzx7fdzqzwx",
  "venue": "HAL",
  "versions": []
}