Vlasov moments, integrable systems and singular solutions
arXiv:0705.3603 · doi:10.1016/j.physleta.2007.08.054
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.
16 pages, no figures. Submitted to Phys. Lett. A
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- Two component integrable systems modelling shallow water waves: the constant vorticity case
- Singular solutions of a modified two-component Camassa-Holm equation
- Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
- Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket
- Higher order Hamiltonian fluid reduction of Vlasov equation
- -Strands
- Double bracket dissipation in kinetic theory for particles with anisotropic interactions
- Vlasov moment flows and geodesics on the Jacobi group
- Geometric dissipation in kinetic equations
- Hamiltonian closures for two-moment fluid models derived from drift-kinetic equations
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