Classical and quantum ensembles via multiresolution: I—BBGKY hierarchy

A fast and efficient numerical–analytical approach is proposed for modeling complex behavior in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for the hierarchy of reduced distribution functions in the variational approach and multiresolution decomposition in polynomial tensor algebras of high-localized states. Numerical modeling shows the creation of various internal structures from localized modes, which are related to localized or chaotic types of behavior and the corresponding pattern (waveleton) formation. The localized pattern is a model for energy confinement state (fusion) in plasma.