{
  "annotation_id": "f094f453-1ee2-4238-abfc-5bd8c208872c",
  "date_created": "2026-03-02T18:00:28.670000Z",
  "date_modified": "2026-03-02T18:00:28.670000Z",
  "file_hash": "8acb417389d3b881dba5d16b5cc8167ebff5d71c1c2b08742b0ede49576edc9a",
  "private": false,
  "record": {
    "abstract": "We develop a general mapping from given kink or pulse shaped travelling-wave\nsolutions including their velocity to the equations of motion on\none-dimensional lattices which support these solutions. We apply this mapping -\nby definition an inverse method - to acoustic solitons in chains with nonlinear\nintersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion\nequations and to discrete nonlinear Schr\\\"odinger systems. Potential functions\ncan be found in at least a unique way provided the pulse shape is reflection\nsymmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we\ndiscuss the relation of our results to the problem of a Peierls-Nabarro\npotential and continuous symmetries. We then generalize our method to higher\ndimensional lattices for reaction-diffusion systems. We find that increasing\nalso the number of components easily allows for moving solutions.",
    "arxiv_id": "patt-sol/9812004",
    "authors": [
      "S. Flach",
      "Y. Zolotaryuk",
      "K. Kladko"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.59.6105",
    "title": "Moving lattice kinks and pulses: an inverse method",
    "url": "https://arxiv.org/abs/patt-sol/9812004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8865ef9e-69b0-4a42-aa3e-b298bf2b6b3f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}