{
  "id": "1506.02309",
  "version": "v1",
  "published": "2015-06-07T20:07:46.000Z",
  "updated": "2015-06-07T20:07:46.000Z",
  "title": "Deformations of non semisimple Poisson pencils of hydrodynamic type",
  "authors": [
    "Alberto Della Vedova",
    "Paolo Lorenzoni",
    "Andrea Savoldi"
  ],
  "comment": "45 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We study deformations of two-component non semisimple Poisson pencils of hydrodynamic type associated with Balinski\\v{\\i}-Novikov algebras. We show that in most cases the second order deformations are parametrized by two functions of a single variable. It turns out that one function is invariant with respect to the subgroup of Miura transformations preserving the dispersionless limit and another function is related to a one-parameter family of truncated structures. In two expectional cases the second order deformations are parametrized by four functions. Among them two are invariants and two are related to a two-parameter family of truncated structures. We also study the lift of deformations of n-component semisimple structures. This example suggests that deformations of non semisimple pencils corresponding to the lifted invariant parameters are unobstructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-07T20:07:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hydrodynamic type",
      "second order deformations",
      "two-component non semisimple poisson pencils",
      "non semisimple pencils",
      "n-component semisimple structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602309D"
    }
  }
}