The twistor theory of Whitham hierarchy

We have generalized the approach in of Dunajski, Mason and Tod [10] and established a 1-1 correspondence between a solution of the universal Whitham hierarchy [23] 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 × CP 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.