{
  "abstract": "The evolution of long wavelength perturbations of traveling wave 2-soliton solutions of the Kadomtsev-Petviashvili II (KP) equation are investigated using modulation theory. An initial-boundary value problem for a system of hyperbolic conservation laws is formulated for amplitude and slope perturbations to soliton legs of the resonant (Y-shaped) and X-shaped KP traveling wave solutions. The vertex where individuated soliton legs coalesce is modeled as a moving free boundary where information between the soliton legs can pass. The linearized hyperbolic system is proven to be well-posed under suitable initial conditions and is solved exactly. In the case of the resonant Y-shaped soliton, all admissible simple (rarefaction) waves of the nonlinear system are characterized. Specific perturbations of Y-waves can lead to the dimensionality of the modulated solution changing, corresponding to a physical geometric change to the multi-soliton pattern. Spontaneous leg deletion and leg creation can occur. The conditions under which the Y-wave modulation system can experience gradient catastrophe are given. Gradient catastrophe is regularized by the formation of a new leg, with an augmented modulation system proposed to describe the growth of the new leg. On the other hand, the X-wave system can be reduced to two independent line soliton modulation systems. These findings reinforce the prevalence and generality of resonant Y-shaped vertices in the KP II system and applications.The theoretical modulation predictions are supported by direct numerical simulations of KP II, which show good agreement with the analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31425",
  "author_total": 2,
  "authors": [
    {
      "name": "Jerry Wang"
    },
    {
      "name": "Mark A. Hoefer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9f7wma5rtcr1h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31425",
  "fulltext_url": null,
  "id": "9f7wma5rtcr1h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31425",
  "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",
      "nlin.PS"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7223267613",
  "pdf_url": "https://arxiv.org/pdf/2610.31425",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9f7wma5rtcr1h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31425",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31425"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Modulation theory of Y- and X-wave Kadomtsev--Petviashvili solitons",
  "title_text": "Modulation theory of Y- and X-wave Kadomtsev--Petviashvili solitons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/9f7wma5rtcr1h",
  "venue": "arXiv",
  "versions": []
}