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Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method

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Konopelchenko, Boris and Martínez Alonso, Luis (2002) Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method. Journal of mathematical physics, 43 (7). pp. 3807-3823. ISSN 0022-2488

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Official URL: http://dx.doi.org/10.1063/1.1481545


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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.

Uncontrolled Keywords:Korteweg-devries equation; Topological field-theory; Quasi-classical limit; Conformal-maps; Kp hierarchy; Systems; Models; Dimensions
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:34420
Deposited On:24 Nov 2015 18:20
Last Modified:10 Dec 2018 15:10

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