Solutions of the Dispersionless Toda Hierarchy Constrained by String   Equations
  Solutions of the Riemann-Hilbert problem implementing the twistorial structure of the dispersionless Toda (dToda) hierarchy are obtained. Two types of string equations are considered which characterize solutions arising in hodograph sectors and integrable structures of two-dimensional quantum gravity and Laplacian growth problems. 
Luis Martinez Alonso and Elena Medina