From Localization to Stochastics in BBGKY Collective Dynamics

Fast and efficient numerical-analytical approach is proposed for modeling complex collective behaviour in accelerator/plasma physics models based on BBGKY hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the bases of polynomial tensor algebras of generalized coherent states/wavelets. We construct the representation for hierarchy of reduced distribution functions via the multiscale decomposition in high-localized eigenmodes. Numerical modeling shows the creation of different internal coherent structures from localized modes, which are related to stable/unstable type of behaviour and corresponding pattern (waveletons) formation.