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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| 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 |
| 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. |
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