Local perturbations of translationally invariant solutions of the Bogolyubov (BBGKY) hierarchy

A study is made of solutions that admit a splitting into a global (spatially homogeneous) and local (integrable)part. The equation obtained for the global part is the original Bogolyubov (BBGKY) hierarchy. The equation for the local part differs from the original hierarchy by the presence of terms that describe the influence of the global part. Compact expressions are obtained for the solution of the equation for the local part under the condition that the global part is a stationary solution of the original equations.