The twistor theory of Whitham hierarchy

We have established a 1-1 correspondence between a solution of the universal Whitham hierarchy and a twistor space. The twistor space consists of a complex surface and a family of complex curves together with a meromorphic 2-form. The solution of the Whitham hierarchy is given by deforming the curve in the surface. By treating the family of algebraic curves in $CP^1 X CP^1$ as a twistor space, we were able to express the deformations of the isomonodromic spectral curve in terms of the deformations generated by the Whitham hierarchy.