%0 Journal Article
%A Mañas Baena, Manuel Enrique
%T S-functions, reductions and hodograph solutions of ther-th dispersionless modified KP and Dym hierarchies
%D 2004
%@ 0305-4470
%U https://hdl.handle.net/20.500.14352/51534
%X 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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