{
  "id": "2301.03919",
  "version": "v1",
  "published": "2023-01-10T11:48:41.000Z",
  "updated": "2023-01-10T11:48:41.000Z",
  "title": "Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus",
  "authors": [
    "Louise Gassot"
  ],
  "categories": [
    "math.AP",
    "nlin.SI"
  ],
  "abstract": "We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus for bell shaped initial data. Using the approximation by truncated Fourier series, we transform the eigenvalue equation for the Lax operator into a problem in the complex plane. Then, we use the steepest descent method to get asymptotic expansions of the Lax eigenvalues. As a consequence, we determine the weak limit of solutions as the dispersion parameter goes to zero, as long as the initial data is an even bell shaped potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-10T11:48:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "benjamin-ono equation",
      "zero-dispersion limit",
      "lax eigenvalues",
      "bell shaped initial data",
      "steepest descent method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}