{
  "abstract": "We study ground-state solutions of the 4th order nonlinear Schrödinger equation with mixed dispersion via the elliptic profile equation $Δ^2 Q + 2a ΔQ + bQ - |Q|^αQ=0$, focusing on symmetry breaking of least-action ground states in 2D in the regime $a=1$, $b=1+ε$, $0<ε\\ll 1$, where nonradiality was proved by Lenzmann and Weth [26]. We establish a quotient-to-mass relation converting small-$ε$ asymptotics of the Weinstein quotient into mass asymptotics, in any dimension and symmetry class. In 1D we prove the sharp small-$ε$ rate for the quotient for every $α>0$ and deduce the rates for the mass, action and potential norm. In two and higher dimensions the same relation, combined with the quotient asymptotics of Lenzmann-Weth [26] and Mandel-Oliveira e Silva [27], gives the mass rates for the Knapp-type nonradial and the radial ground states. The resulting threshold $α_K(d)=8/(d+1)$ coincides for $d\\leq3$ with the existence of normalized minimizers threshold of Fernández-Jeanjean-Mandel-Mariş [16], connecting the least-action and mass-constrained formulations. We complement this with a detailed numerical study. For the cubic nonlinearity we construct a nonradial branch from a Knapp-type example, compare it with radial and angular-mode branches, and verify the predicted rates. For the quartic nonlinearity, turning points and branching are present in the mass-energy diagrams in radial or two- and four-peak nonradial solutions. Here, although least-action ground states are nonradial for small $ε$, the normalized ground states of the same mass appear radial, a consequence of branching. For $α\\geq4$ we find only radial ground states, consistent with the conjectured sharp form of the Stein-Tomas inequality on $\\mathbb S^1$, equivalent to the radial and nonradial masses having the same leading coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13783",
  "author_total": 2,
  "authors": [
    {
      "name": "Christian Klein"
    },
    {
      "name": "Svetlana Roudenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qer71pwbpx32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13783",
  "fulltext_url": null,
  "id": "7qer71pwbpx32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13783",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213318955",
  "pdf_url": "https://arxiv.org/pdf/2609.13783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qer71pwbpx32.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Ground states to bi-harmonic nonlinear Schrödinger equations with competing dispersion",
  "title_text": "Ground states to bi-harmonic nonlinear Schrödinger equations with competing dispersion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7qer71pwbpx32",
  "venue": "arXiv",
  "versions": []
}