{
  "id": "1306.4192",
  "version": "v1",
  "published": "2013-06-18T13:37:14.000Z",
  "updated": "2013-06-18T13:37:14.000Z",
  "title": "Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems",
  "authors": [
    "B. G. Konopelchenko",
    "G. Ortenzi"
  ],
  "comment": "18 pages, no figures",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "Structure and properties of families of critical points for classes of functions $W(z,\\bar{z})$ obeying the elliptic Euler-Poisson-Darboux equation $E(1/2,1/2)$ are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented There are the extended dispersionless Toda/nonlinear Schr\\\"{o}dinger hierarchies, the \"inverse\" hierarchy and equations associated with the real-analytic Eisenstein series $E(\\beta,\\bar{{\\beta}};1/2)$among them. Specific bi-Hamiltonian structure of these equations is also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-18T13:37:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic euler-poisson-darboux equation",
      "critical points",
      "integrable systems",
      "real-analytic eisenstein series",
      "corresponding integrable quasi-linear differential systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/46/48/485204",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Dec",
      "volume": 46,
      "number": 48,
      "pages": 485204
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhA...46V5204K"
    }
  }
}