  We study a class of nonlocal systems which can be described by a local scalar
field diffusing in an auxiliary radial dimension. As examples p-adic, open and
boundary string field theory are considered on Minkowski,
Friedmann-Robertson-Walker and Euclidean metric backgrounds. Starting from
distribution-like initial field configurations which are constant almost
everywhere, we construct exact and approximate nonlocal solutions. The
Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean
kink of supersymmetric open string field theory as an instanton. Some relations
between solutions of different string theories are highlighted also thanks to a
reformulation of nonlocal systems as fixed points in a renormalization group
flow.
