Publication: S-functions, reductions and hodograph solutions of the
r-th dispersionless modified KP and Dym hierarchies
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2004-11-12
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IOP Publishing
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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.
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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.
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