{
  "annotation_id": "aa52f333-5df4-49ab-9dcd-4d00783eeeea",
  "date_created": "2026-03-02T18:02:50.752000Z",
  "date_modified": "2026-03-02T18:02:50.752000Z",
  "file_hash": "7098c8d093b5a9a48876c1ffaf45f6331c7e8f390a345212ed7131e3e71571ee",
  "private": false,
  "record": {
    "abstract": "We study confined solutions of certain evolutionary partial differential\nequations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian\nsystems for quadratic Hamiltonians defined on the dual of the Lie algebra of\nvector fields on the real line. These systems are also Euler-Poincare equations\nfor geodesic motion on the diffeomorphism group in the sense of the Arnold\nprogram for ideal fluids, but where the kinetic energy metric is different from\nthe L2 norm of the velocity. These pde possess a finite-dimensional invariant\nmanifold of particle-like (measure-valued) solutions we call ``pulsons.\u0027\u0027 We\nsolve the particle dynamics of the two-pulson interaction analytically as a\ncanonical Hamiltonian system for geodesic motion with two degrees of freedom\nand a conserved momentum. The result of this two-pulson interaction for\nrear-end collisions is elastic scattering with a phase shift, as occurs with\nsolitons. In contrast, head-on antisymmetric collisons of pulsons tend to form\nsingularities.",
    "arxiv_id": "solv-int/9903007",
    "authors": [
      "O. B. Fringer",
      "D. D. Holm"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Integrable vs Nonintegrable Geodesic Soliton Behavior",
    "url": "https://arxiv.org/abs/solv-int/9903007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bca2bfef-ea70-4b33-bd45-0468dc7341de",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}