The Existence of Stable BGK Waves

Abstract

The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisionless plasma, and the BGK waves are its famous exact steady solutions. They play an important role on the long time dynamics of a collisionless plasma as potential “final states” or “attractors”, thanks to many numerical simulations and observations. Despite their importance, the existence of stable BGK waves has been an open problem since the discovery of BGK waves in 1957. In this paper, linearly stableBGK waves are constructed near homogeneous states.