{
  "annotation_id": "32fa1a1a-71dc-4a0e-825c-9c0352207008",
  "date_created": "2026-03-02T18:00:28.607000Z",
  "date_modified": "2026-03-02T18:00:28.607000Z",
  "file_hash": "83b60e52833ddd3702341756cbb5eb42d37208af3ad9b1f431e128507df30fda",
  "private": false,
  "record": {
    "abstract": "In a recent paper Goriely considers the one--dimensional scalar\nreaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction\nterm $f(u)$ and conjectures the existence of a relation between a global\nresonance of the hamiltonian system $ u_{xx} + f(u) = 0$ and the asymptotic\nspeed of propagation of fronts of the reaction diffusion equation. Based on\nthis conjecture an explicit expression for the speed of the front is given. We\ngive a counterexample to this conjecture and conclude that additional\nrestrictions should be placed on the reaction terms for which it may hold.",
    "arxiv_id": "patt-sol/9606004",
    "authors": [
      "J. Cisternas",
      "M. C. Depassier"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.55.3701",
    "journal_ref": "Phys. Rev. E., 55 (1997) 3701",
    "title": "On a Conjecture of Goriely for the Speed of Fronts of the   Reaction--Diffusion Equation",
    "url": "https://arxiv.org/abs/patt-sol/9606004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "be7f93cc-65a9-4f67-977a-a0b2efbcad32",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}