{
  "id": "2406.09743",
  "version": "v1",
  "published": "2024-06-14T06:19:35.000Z",
  "updated": "2024-06-14T06:19:35.000Z",
  "title": "Stability of the Toda equations related to a perturbed $R_i$ type recurrence relation",
  "authors": [
    "Vinay Shukla",
    "A. Swaminathan"
  ],
  "comment": "15 pages, 19 figures",
  "categories": [
    "math.CA",
    "nlin.SI"
  ],
  "abstract": "In this manuscript, a modified $R_I$ type recurrence relation is considered whose recurrence coefficients are perturbed by addition or multiplication of a constant. The perturbed system of recurrence coefficients is represented by Toda lattice equations, which are derived. These equations are then represented in a matrix form. With the help of this matrix representation, a known Lax pair is recovered. Inferences about the stability of resulting perturbed system of Toda equations are drawn based on numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-14T06:19:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "15A24",
      "37K10"
    ],
    "keywords": [
      "type recurrence relation",
      "toda equations",
      "recurrence coefficients",
      "perturbed system",
      "toda lattice equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}