Non-perturbative solutions of hierarchies of evolution equations for colliding particles

The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations for observables and a state is used to establish the generating operators of expansions representing solutions of the Cauchy problems of the BBGKY hierarchy (Bogolyubov–Born–Green–Kirkwood–Yvon) as well as of the dual BBGKY hierarchy, respectively.