The partial derivative-approach to the dispersionless KP hierarchy

The dispersionless limit of the scalar nonlocal a-problem is derived. It is given by a special class of nonlinear first-order equations. A quasiclassical version of the partial derivative -dressing method is presented. It is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of Beltrami-type equations. The universal Whitham hierarchy and, in particular, the dispersionless KP hierarchy turn out to be rings of symmetries for the quasiclassical partial derivative -problem.