{
  "abstract": "We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor $z$ characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters $α$ and $β$ and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for $αβ=1$, whereas for $αβ\\neq 1$ parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate small residual disturbances and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17211",
  "author_total": 4,
  "authors": [
    {
      "name": "A. R. Aguirre"
    },
    {
      "name": "H. Blas"
    },
    {
      "name": "H. F. Callisaya"
    },
    {
      "name": "M. C. de Oliveira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6phk9p6zym0w3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17211",
  "fulltext_url": null,
  "id": "6phk9p6zym0w3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17211",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "nlin.SI"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.17211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6phk9p6zym0w3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2608.17211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17211"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation",
  "title_text": "Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6phk9p6zym0w3",
  "venue": "arXiv",
  "versions": []
}