{
  "abstract": "We obtain exact solutions of a system of two third--order ordinary differential equations arising in the classification of diagonalizable hydrodynamic chains. We show that the system admits a four--dimensional solvable Lie algebra of point symmetries. Although this algebra is not large enough for the complete integrability by quadratures, it enables a reduction to a two--dimensional first--order system. A further symmetry reduction leads to an Abel equation whose implicit solutions define a family of algebraic curves. By analysing their singular cases and deriving rational parametrizations, we obtain the solutions to the reduced system in parametric form. The solutions to the original third--order system are then reconstructed by four successive quadratures using Lie--Bianchi's theorem. The resulting families contain a previously known specific solution as a particular case and provide new diagonalizable hydrodynamic chains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Beltrán de la Flor"
    },
    {
      "name": "Adrián Ruiz"
    },
    {
      "name": "Concepción Muriel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52tryjtf5cptb.bib",
  "cited_by": 0,
  "doi": "10.46298/ocnmp.18629",
  "fulltext_url": null,
  "id": "52tryjtf5cptb",
  "issns": [
    "2802-9356"
  ],
  "landing_url": "https://hal.science/hal-05670162v2",
  "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"
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    [
      "hal",
      "1.math.math-ca"
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      "openalex",
      "3109|Nonlinear Waves and Solitons"
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  "openalex": "W7166490732",
  "pdf_url": "https://hal.science/hal-05670162/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "International Society of Nonlinear Mathematical Physics",
  "ris": "https://research.draconitic.com/paper/52tryjtf5cptb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05670162",
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      "url": "https://hal.science/hal-05670162v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ca",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Exact solutions to a system of ODEs arising in classification of diagonalizable hydrodynamic chains",
  "title_text": "Exact solutions to a system of ODEs arising in classification of diagonalizable hydrodynamic chains",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/52tryjtf5cptb",
  "venue": "Open Communications in Nonlinear Mathematical Physics",
  "versions": []
}