Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, UMR CNRS 7351, Parc Valrose 06108 Nice Cedex 02, France and Institut Universitaire de France, 75005 Paris, France.
Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, UMR CNRS 7351, Parc Valrose 06108 Nice Cedex 02, France.
Phys Rev E. 2016 Apr;93:042207. doi: 10.1103/PhysRevE.93.042207. Epub 2016 Apr 14.
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
我们研究了发生在星系模型中的非均匀定态的 Vlasov 方程的非振动分岔，或者等离子体物理中的 Bernstein-Greene-Kruskal 模式。通过不稳定流形展开，我们表明在一维空间中，动力学对初始微扰非常敏感：不稳定性可能在小振幅处饱和——推广了等离子体物理中的“捕获缩放”——或者可能增长，从而对系统产生大规模的改变。此外，共振被强烈抑制，导致与均匀情况不同的现象。这些分析结果通过具有余弦相互作用势的直接数值模拟得到了说明和扩展。
