{
  "id": "1903.12636",
  "version": "v1",
  "published": "2019-03-29T17:37:56.000Z",
  "updated": "2019-03-29T17:37:56.000Z",
  "title": "Recovery of zeroth order coefficients in non-linear wave equations",
  "authors": [
    "Ali Feizmohammadi",
    "Lauri Oksanen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the resolution of an inverse problem related to the recovery of a scalar (potential) function $V$ from the source to solution map, $L_V$, of the semi-linear equation $(-\\Box_{g}+V)u+u^3=0$ on a globally hyperbolic Lorentzian manifold $(M,g)$. We first study the simpler model problem where the geometry is the Minkowski space and prove the uniqueness of $V$ through the use of geometric optics and a three-fold wave interaction arising from the cubic non-linearity. Subsequently, the result is generalized to globally hyperbolic Lorentzian manifolds by using Gaussian beams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-29T17:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "zeroth order coefficients",
      "non-linear wave equations",
      "globally hyperbolic lorentzian manifold",
      "simpler model problem",
      "three-fold wave interaction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}