Abstract
The quasiclassical limit of the scalar nonlocal ∂̄-problem is derived and a quasiclassical version of the ∂̄-dressing method is presented. Dispersionless Kadomtsev–Petviashvili (KP), modified KP, and dispersionless two-dimensional Toda lattice (2DTL) hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy is nothing but the ring of symmetries for the quasiclassical ∂̄-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.
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