{
  "abstract": "The infinite-dimensional symmetry algebras of integrable systems in $(2+1)$ dimensions exhibit a remarkable reduction property when restricted to finite-dimensional multi-soliton manifolds. In this paper, we systematically investigate this phenomenon for the Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili equations. For the Kadomtsev-Petviashvili equation, we analyze both the $K$-symmetry and the $τ$-symmetry hierarchies. It is shown that for any $n$-soliton solution, each higher-order $K$-symmetry generator reduces to a linear combination of the $n$ independent translational symmetries $σ_{ξ_{m0}}$ associated with the individual soliton phase shifts, where the coefficients are precisely the dispersion relations evaluated at the soliton parameters. Closed-form expressions for odd- and even-order $K$-symmetries are derived, and determinant representations are provided to characterize the reduction systematically. For the \\(τ\\)-symmetries, each \\(τ_n\\) becomes a linear combination of the three fundamental soliton symmetries \\(σ_{k_m}\\), \\(σ_{l_m}\\), and \\(σ_{ξ_{m0}}\\), with coefficients that are rational functions of soliton parameters \\(k_m\\) and \\(l_m\\). These results are further extended to the modified Kadomtsev-Petviashvili equation, where analogous reduction patterns are established. This work establishes a direct and intrinsic link between the algebraic structure of infinite symmetries and the spectral properties of soliton solutions, offering a unified physical interpretation: the infinite set of higher-order symmetries generates linear superpositions of elementary soliton translations, weighted by powers of the wave numbers and dispersion coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29770",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiazhi Hao"
    },
    {
      "name": "Mingxia Ji"
    },
    {
      "name": "Senyue Lou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8a2dsn0zcst2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29770",
  "fulltext_url": null,
  "id": "c8a2dsn0zcst2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29770",
  "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": "W7223224789",
  "pdf_url": "https://arxiv.org/pdf/2610.29770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8a2dsn0zcst2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29770"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "From infinite symmetries to multi-soliton manifolds: dispersion-driven reduction for the KP and mKP equations",
  "title_text": "From infinite symmetries to multi-soliton manifolds: dispersion-driven reduction for the KP and mKP equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/c8a2dsn0zcst2",
  "venue": "arXiv",
  "versions": []
}