Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method

Details Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method

2001-05-31

arxiv.org/abs/nlin/0105071v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex file,19 pages

Scientific paper

The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy it is nothing but the ring of symmetries for the quasi-classical dbar-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.

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