{
  "abstract": "The pseudo-parabolic term $u_{xxt}$ serves as a canonical example of higher-order viscosity that provides effective regularization while capturing the refined physical mechanism. How it alters the dynamics of prototype equations remains a fundamental issue, which is not yet fully understood. The goal of this paper is to show that this term induces a sharp transition in traveling wave structure, via studying the pseudo-parabolic Fisher-KPP equation $$ u_t - τu_{xxt} = D u_{xx} + u(1-u). $$ We completely characterize how the parameter ratio $τ/D$ acts as a critical switch: it preserves the monotonic structure of classical traveling waves when $τ/D \\leq 1$, yet it triggers a qualitative shift to oscillatory traveling waves when $τ/D > 1$. Numerical simulations support these findings. The threshold $τ/D=1$ thus captures the dual role of the pseudo-parabolic term: it acts as a structure-preserving viscosity when small, but when large it reflects dominant capillary hysteresis, generating the oscillations that explain the saturation overshoot, a phenomenon that contradicts classical diffusion models yet is widely observed in two-phase flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34368",
  "author_total": 4,
  "authors": [
    {
      "name": "Yang Cao"
    },
    {
      "name": "Haomeng Chen"
    },
    {
      "name": "Chunhua Jin"
    },
    {
      "name": "Jingxue Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fawqrbaf40ged.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34368",
  "fulltext_url": null,
  "id": "fawqrbaf40ged",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34368",
  "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",
      "math.AP"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7214759646",
  "pdf_url": "https://arxiv.org/pdf/2609.34368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fawqrbaf40ged.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.34368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A Critical Value for the Viscosity Coefficient: Triggering Oscillatory Traveling Waves in the Pseudo-parabolic Fisher-KPP Equation",
  "title_text": "A Critical Value for the Viscosity Coefficient: Triggering Oscillatory Traveling Waves in the Pseudo-parabolic Fisher-KPP Equation",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/fawqrbaf40ged",
  "venue": "arXiv",
  "versions": []
}