{
  "abstract": "The dynamic acoustic scattering system is governed by the wave equation $u_{tt}-Δu+qu=0$ in $\\Bbb R^3,\\,\\,\\,-\\infty<t<\\infty$, with a compactly supported potential $q$ and infinitely distant sources (controls) $f$, which initiate incoming spherical waves $u=u^f(x,t)$ provided $u^f\\big|_{|x|<-t,\\,\\,\\,t<0}=0$. These waves are focused at $x=0$ and fill up the whole space at the moment $t=0$. The system is {\\it controllable} if the set of waves $u^f(\\cdot,0)$ produced by all finite energy controls $f$, covers the space $L_2(\\Bbb R^3)$. As we show, if the Hamiltonian $H=-Δ+q$ has the bound states, then in the space the points $a$ appear such that the system, being refocused at $x=a$, loses controllability. The latter leads to a physical effect: the waves $u^f$ of finite energy appear, which vanish simultaneously in the past and future cones $|x|<\\pm\\, t$ and leave the region of inhomogeneity of $q$ without reverberation. This effect has some similarities with the wavefront reversal (Time Reversing Mirror), but is more meaningful from a mathematical point of view.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03536",
  "author_total": 2,
  "authors": [
    {
      "name": "Mikhail I. Belishev"
    },
    {
      "name": "Aleksei F. Vakulenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3v73sn972tyq1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03536",
  "fulltext_url": null,
  "id": "3v73sn972tyq1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03536",
  "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.MP"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7208713328",
  "pdf_url": "https://arxiv.org/pdf/2609.03536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3v73sn972tyq1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Controllability, returning waves and scattering without reverberation in 3D acoustic dynamic system",
  "title_text": "Controllability, returning waves and scattering without reverberation in 3D acoustic dynamic system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/3v73sn972tyq1",
  "venue": "arXiv",
  "versions": []
}