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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Cited by in corpus (5)
- Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
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- Kinetic models of heterogeneous dissipation