{
  "id": "2212.10130",
  "version": "v1",
  "published": "2022-12-20T09:58:09.000Z",
  "updated": "2022-12-20T09:58:09.000Z",
  "title": "Solutions of the wave equation for commuting flows of dispersionless PDEs",
  "authors": [
    "Natale Manganaro",
    "Alessandra Rizzo",
    "Pierandrea Vergallo"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this article, we apply the reduction procedure of differential constraints to obtain some solutions of the wave equation with non-constant speed depending on the field variables. We discuss the results obtained in the perspective of commuting flows in integrable systems, according to Dubrovin's theory of deformations of PDEs. Finally, we present some examples of Hamiltonian integrable systems and find some implicit solutions via Tsarev's generalized hodograph method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-20T09:58:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave equation",
      "commuting flows",
      "dispersionless pdes",
      "tsarevs generalized hodograph method",
      "reduction procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}