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S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

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Mañas Baena, Manuel (2004) S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies. Journal of physics A: Mathematical and general, 37 (46). pp. 11191-11221. ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/37/46/007




Abstract

We introduce an S-function formulation for the recently found rth dispersionless modified KP and rth dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the S-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic-type systems. In particular, for the one-component and two-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.


Item Type:Article
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©IOP Publishing.
The author is in debt with Luis Martínez Alonso and Elena Medina, coauthors of [18], paper on which the present one is partially based. Partial economical support from Dirección General de Enseñanza Superior e Investigación Científica no BFM2002-01607 is also acknowledge.

Uncontrolled Keywords:Topological field-theory; R-Matrix theory; Integrable hierarchies; Whitham hierarchy; Additional symmetries; Conformal-maps; Dkp equation; Tau-function; Systems; Deformations
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32555
Deposited On:27 Jul 2015 10:03
Last Modified:10 Dec 2018 15:09

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