Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method
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2002
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American Institute of Physics
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Abstract
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.
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©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.