  Solutions to the Riemann-Hilbert problems with irregular singularities
naturally associated to semisimple Frobenius manifold structures on Hurwitz
spaces (moduli spaces of meromorphic functions on Riemann surfaces) are
constructed. The solutions are given in terms of meromorphic bidifferentials
defined on the underlying Riemann surface. The relationship between different
classes of Frobenius manifold structures on Hurwitz spaces (real doubles,
deformations) is described on the level of the corresponding Riemann-Hilbert
problems.
