  We describe all smooth solutions of the two-function tt*-Toda equations (a
version of the tt* equations, or equations for harmonic maps into
SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and
(iii) monodromy data. This allows us to find all solutions with integral Stokes
data. These include solutions associated to nonlinear sigma models (quantum
cohomology) or Landau-Ginzburg models (unfoldings of singularities), as
conjectured by Cecotti and Vafa.
