2006/03/26 by John Gibbons, Darryl D. Holm, Gibbons, John +3
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #nlin.CD #nlin.PS
paper · pdf · doi:10.48550/arxiv.nlin/0603060
20 pages, no figures
openalex publication_date 2006/03/26 · arxiv created 2006/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. That is, the evolution of the moments of the Vlasov PDF is also coadjoint motion. We find that \it geodesic coadjoint motion of the Vlasov moments with respect to powers of the single-particle momentum admits singular (weak) solutions concentrated on embedded subspaces of physical space. The motion and interactions of these embedded subspaces are governed by canonical Hamiltonian equations for their geodesic evolution.