{
  "id": "1407.7743",
  "version": "v2",
  "published": "2014-07-29T14:47:41.000Z",
  "updated": "2015-01-12T17:41:48.000Z",
  "title": "Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system",
  "authors": [
    "L. Cortés Vega",
    "A. Restuccia",
    "A. Sotomayor"
  ],
  "comment": "In this second version of 23 pages we obtain static solutions which play the role of a background for the system. We also discuss about the regularity of the solutions. We add some figures illustrating the solutions, including the one solitonic solution interacting with the static-background one. We modify the abstract in view of these improvements",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We introduce a parametric coupled KdV system which contains, for particular values of the parameter, the complex extension of the KdV equation and one of the Hirota-Satsuma integrable systems. We obtain a generalized Gardner transformation and from the associated $\\varepsilon$- deformed system we get the infinite sequence of conserved quantities for the parametric coupled system. We also obtain a B\\\"{a}cklund transformation for the system. We prove the associated permutability theorem corresponding to such transformation and we generate new multi-solitonic and periodic solutions for the system depending on several parameters. We show that for a wide range of the parameters the solutions obtained from the permutability theorem are regular solutions. Finally we found new multisolitonic solutions propagating on a non-trivial regular static background.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T14:47:41.000Z",
      "abstract": "We obtain a B\\\"acklund transformation for a parametric coupled KdV system. We prove the associated permutability theorem corresponding to such transformation and we generate new multi-solitonic and periodic solutions for the system. We introduce a generalized Gardner transformation and obtain from the associated $\\varepsilon$- deformed system the infinite sequence of conserved quantities for the parametric coupled system.",
      "comment": "13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-12T17:41:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parametric coupled korteweg-de vries system",
      "bäcklund transformation",
      "multisolitonic solutions",
      "parametric coupled kdv system",
      "parametric coupled system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1309625,
      "adsabs": "2014arXiv1407.7743C"
    }
  }
}