{
  "abstract": "By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric $ϕ^4$-like coupled equations in $x$ and $t$, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) $\\mathcal{PT}$-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36891",
  "author_total": 4,
  "authors": [
    {
      "name": "Thokala Soloman Raju"
    },
    {
      "name": "T. Shreecharan"
    },
    {
      "name": "Avinash Khare"
    },
    {
      "name": "Avadh Saxena"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9v5aa2wzsv29n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36891",
  "fulltext_url": null,
  "id": "9v5aa2wzsv29n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36891",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
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  ],
  "openalex": "W7224125941",
  "pdf_url": "https://arxiv.org/pdf/2610.36891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9v5aa2wzsv29n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence",
  "title_text": "Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/9v5aa2wzsv29n",
  "venue": "arXiv",
  "versions": []
}