arXiv 0705.36032007-05-24nlin.SImath-phmath.MPphysics.acc-phphysics.plasm-ph

Vlasov moments, integrable systems and singular solutions

John Gibbons, Darryl D Holm, Cesare Tronci

备注：: 16 pages, no figures. Submitted to Phys. Lett. A
DOI：: 10.1016/j.physleta.2007.08.054

英文摘要：

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.

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