{
  "abstract": "We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schrödinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\\to\\infty$, with the discrete spectrum confined to two segments $Σ_1$ and $Σ_2$. In particular, our framework does not require the discrete spectrum to be confined to the imaginary axis. By combining the nonlinear steepest descent method with an appropriate $g$-function mechanism, we show that, as $x\\to-\\infty$, the soliton gas is asymptotically described by a finite-gap elliptic solution with constant coefficients. In the large-time regime $t\\to+\\infty$, we assume that the endpoint $F$ lies on the trajectory of $H(ξ)$ with $ξ=\\frac{x}{2t}\\in(-E_1-\\sqrt{2}E_2,-E_1)$, namely, $F=H(\\hatξ)$, $\\hatξ\\in (-E_1-\\sqrt{2}E_2,-E_1)$. Under this assumption, we prove that the solution exhibits distinct asymptotic behaviors in different regions of the variable $ξ=\\frac{x}{2t}$. More precisely, there exist an exponentially decaying region $ξ\\in(-E_1,+\\infty)$, a modulated elliptic-wave region $ξ\\in(\\hatξ,-E_1)$, and an unmodulated elliptic-wave region $ξ\\in(-\\infty,\\hatξ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21091",
  "author_total": 3,
  "authors": [
    {
      "name": "Dedi Yan"
    },
    {
      "name": "Xianguo Geng"
    },
    {
      "name": "Jiao Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar241faq3mmj1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21091",
  "fulltext_url": null,
  "id": "ar241faq3mmj1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21091",
  "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",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7162011005",
  "pdf_url": "https://arxiv.org/pdf/2605.21091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar241faq3mmj1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2605.21091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21091"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Large-space and Large-time Asymptotics for the Focusing Nonlinear Schrödinger Soliton Gas",
  "title_text": "Large-space and Large-time Asymptotics for the Focusing Nonlinear Schrödinger Soliton Gas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/ar241faq3mmj1",
  "venue": "arXiv",
  "versions": []
}