Vlasov moments, integrable systems and singular solutions

2007/05/24 by John Gibbons, Darryl D. Holm, Darryl D Holm +1 · 5 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Oceanographic and Atmospheric Processes #Quantum chaos and dynamical systems #math-ph #math.MP #nlin.SI #physics.acc-ph #physics.plasm-ph

paper · pdf · doi:10.1016/j.physleta.2007.08.054

16 pages, no figures. Submitted to Phys. Lett. A

arxiv created 2007/05/24 · openalex publication_date 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the operation of taking the moments of the Vlasov PDF preserves the Lie-Poisson structure. The individual particle motions correspond to singular solutions of the Vlasov equation. The paper focuses on singular solutions of the problem of geodesic motion of the Vlasov moments. These singular solutions recover geodesic motion of the individual particles.

Citations

• Geometric dissipation in kinetic equations

Cited by

• Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket
• Double-bracket dissipation in kinetic theory for particles with anisotropic interactions
• Vlasov moment flows and geodesics on the Jacobi group
• Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics
• Higher-order Hamiltonian fluid reduction of Vlasov equation

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