  We show that a certain class of nonlocal scalar models, with a kinetic
operator inspired by string field theory, is equivalent to a system which is
local in the coordinates but nonlocal in an auxiliary evolution variable. This
system admits both Lagrangian and Hamiltonian formulations, and its Cauchy
problem and quantization are well-defined. We classify exact nonperturbative
solutions of the localized model which can be found via the diffusion equation
governing the fields.
