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

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

2004-05-12

arxiv.org/abs/nlin/0405028v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel packages

Scientific paper

10.1088/0305-4470/37/46/007

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th 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 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.

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