{
  "id": "0805.3219",
  "version": "v1",
  "published": "2008-05-21T08:06:34.000Z",
  "updated": "2008-05-21T08:06:34.000Z",
  "title": "The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds",
  "authors": [
    "Eiji Onodera"
  ],
  "comment": "23pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We present a time-local existence theorem of the initial value problem for a third-order dispersive evolution equation for open curves on compact almost Hermitian manifolds arising in the geometric analysis of vortex filaments. This equation causes the so-called loss of one-derivative since the target manifold is not supposed to be a K\\\"ahler manifold. We overcome this difficulty by using a gauge transformation of a multiplier on the pull-back bundle to eliminate the bad first order terms essentially.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-21T08:06:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q53",
      "53C44"
    ],
    "keywords": [
      "initial value problem",
      "third-order dispersive flow",
      "hermitian manifolds",
      "third-order dispersive evolution equation",
      "time-local existence theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.3219O"
    }
  }
}