Konopelchenko, BorisMartínez Alonso, Luis2023-06-202023-06-202002-070022-248810.1063/1.1481545https://hdl.handle.net/20.500.14352/59825©2002 American Institute of Physics. This work has been done in the framework of Grant No. INTAS-99-1782. B.K. was supported in part by the grant COFIN 2000 ‘‘Sintesi.’’ L.M.A. has supported in part by CICYT Proyecto No. PB98-0821. B.K. is grateful to the Departamento de Fisica Teorica II Universidad Complutense for kind hospitality during which this paper was basically written.The quasiclassical limit of the scalar nonlocal δ̅ -problem is derived and a quasiclassical version of the δ̅-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 δ̅-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.engjournal articlehttp://dx.doi.org/10.1063/1.1481545http://scitation.aip.orgopen access51-73Korteweg-devries equationTopological field-theoryQuasi-classical limitConformal-mapsKp hierarchySystemsModelsDimensionsFísica-Modelos matemáticosFísica matemática