{
  "abstract": "We study the one-dimensional nonlinear Schrödinger system \\[ -u_i''-2\\Big(\\sum_{k=1}^N u_k^2\\Big)^{p-1}u_i=μ_i u_i \\quad \\mbox{in } \\ \\mathbb R,\\ \\ i=1,2,\\cdots,N, \\tag{S} \\] where $u=(u_1,\\cdots,u_N)\\in H^1(\\mathbb{R})^N$, $μ_1\\leqμ_2\\leq\\cdots\\leqμ_N<0$, $1<p<3$ and $N\\geq 2$ are arbitrary. For the cubic case where $p=2$ and $N\\ge 2$, we establish the following structural results of the system $(S)$: (i) all nontrivial solutions can be classified completely; (ii) the linearized operator at any nontrivial solution is non-degenerate; (iii) exact $L^2$-mass formulas of all nontrivial solutions are derived in terms of distinct Lagrange multipliers $μ_i$. As the applications of the above structural results, we first show that the system $(S)$ with $p=2$ does not have any orthonormal solution for any $N\\ge2$. We then investigate a fermionic variational problem $J_N(p)$ with $N\\ge2$, whose minimizers correspond to ground states of the system $(S)$ under orthonormal constraints. More precisely, we prove that there exists a sufficiently small $δ_N>0$ such that $J_N(p)$ is attained for any $p\\in(2-δ_N,2)$, whereas $J_N(p)$ is not attained for any $p\\in[2,2+δ_N)$. These settle some conjectures of [Gontier--Lewin--Nazar, ARMA, 2021] and [Frank--Gontier--Lewin, CMP, 2021].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17941",
  "author_total": 4,
  "authors": [
    {
      "name": "Bin Chen"
    },
    {
      "name": "Yujin Guo"
    },
    {
      "name": "Yong Luo"
    },
    {
      "name": "Juncheng Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0qmehv3beq9fc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17941",
  "fulltext_url": null,
  "id": "0qmehv3beq9fc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17941",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221814218",
  "pdf_url": "https://arxiv.org/pdf/2610.17941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0qmehv3beq9fc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Cubic Nonlinear Schrödinger Systems and Orthonormal Fermionic Ground States in $\\mathbb R$",
  "title_text": "Cubic Nonlinear Schrödinger Systems and Orthonormal Fermionic Ground States in ℝ",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/0qmehv3beq9fc",
  "venue": "arXiv",
  "versions": []
}