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

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 t...

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Bibliographic Details
Author: Mañas Baena, Manuel Enrique
Format: article
Publication Date:2004
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/51534
Online Access:https://hdl.handle.net/20.500.14352/51534
Access Level:Open access
Keyword:51-73
Topological field-theory
R-Matrix theory
Integrable hierarchies
Whitham hierarchy
Additional symmetries
Conformal-maps
Dkp equation
Tau-function
Systems
Deformations
Física-Modelos matemáticos
Física matemática
Description
Summary: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.