{
  "abstract": "We study the one-dimensional Zakharov-Rubenchik system with periodic initial conditions. This system models the interaction of low-frequency waves with high-frequency waves in different physical phenomena. Using semigroup theory, we prove the global well-posedness of the associated linear equation in $H^q(\\mathbb{T})\\times H^s(\\mathbb{T})\\times H^{s+1}(\\mathbb{T})$, $q,s \\in \\mathbb{R}$. Subsequently, we consider the modified Zakharov-Rubenchik system and, by means of a change of variables and the Banach Fixed Point Theorem, we obtain local well-posedness in the space $H^s(\\mathbb{T})\\times H^s(\\mathbb{T})\\times H^{s+1}(\\mathbb{T})$, $s>3/2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14158",
  "author_total": 2,
  "authors": [
    {
      "name": "Yeison Alejandro Gómez Hernández"
    },
    {
      "name": "Juan Carlos Cordero Ceballos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ama6sx7schgrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14158",
  "fulltext_url": null,
  "id": "ama6sx7schgrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14158",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213244651",
  "pdf_url": "https://arxiv.org/pdf/2609.14158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ama6sx7schgrb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Periodic Solutions of the Zakharov-Rubenchik System",
  "title_text": "On Periodic Solutions of the Zakharov-Rubenchik System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/ama6sx7schgrb",
  "venue": "arXiv",
  "versions": []
}