String equations in Whitham hierarchies: tau-functions and Virasoro   constraints
  A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated. 
Luis Martinez Alonso, Elena Medina and Manuel Manas