The twistor theory of Whitham hierarchy

Details The twistor theory of Whitham hierarchy The twistor theory of Whitham hierarchy

2005-10-07

arxiv.org/abs/nlin/0510013v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages

Scientific paper

10.1016/j.geomphys.2005.11.017

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.

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