Genus-zero Whitham hierarchies in conformal-map dynamics
arXiv:nlin/0609037 · doi:10.1016/j.physletb.2006.08.082
Abstract
A scheme for solving quasiclassical string equations is developped to prove that genus-zero Whitham hierarchies describe the deformations of planar domains determined by rational conformal maps. This property is applied in normal matrix models to show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are governed by genus-zero Whitham hierarchies.
12 pages, 3 figures
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