  We study Ricci flows of some classes of physically valuable solutions in
Einstein and string gravity. The anholonomic frame method is applied for
generic off-diagonal metric ansatz when the field/ evolution equations are
transformed into exactly integrable systems of partial differential equations.
The integral varieties of such solutions, in four and five dimensional gravity,
depend on arbitrary generation and integration functions of one, two and/ or
three variables. Certain classes of nonholonomic frame constraints allow us to
select vacuum and/or Einstein metrics, to generalize such solutions for
nontrivial string (for instance, with antisymmetric torsion fields) and matter
field sources. A very important property of this approach (originating from
Finsler and Lagrange geometry but re-defined for semi-Riemannian spaces) is
that new classes of exact solutions can be generated by nonholonomic
deformations depending on parameters associated to some generalized Geroch
transforms and Ricci flow evolution. In this paper, we apply the method to
construct in explicit form some classes of exact solutions for multi-parameter
Einstein spaces and their nonholonomic Ricci flows describing evolutions/
interactions of solitonic pp-waves and deformations of the Schwarzschild
metric. We explore possible physical consequences and speculate on their
importance in modern gravity.
