RT Journal Article
T1 On the Whitham hierarchy: dressing scheme, string equations and additional symmetries
A1 Mañas Baena, Manuel Enrique
A1 Medina, Elena
A1 Martínez Alonso, Luis
AB A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particularly important function, related to the tau-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for a convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Bentley gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized.
PB IOP Publishing
SN 0305-4470
YR 2006
FD 2006-03-10
LK https://hdl.handle.net/20.500.14352/51533
UL https://hdl.handle.net/20.500.14352/51533
LA eng
NO ©IOP Publishing.Partial economical support from Dirección General de Enseñanza Superior e Investigación Científica no BFM2002-01607, from European Science Foundation: MISGAM and from Marie Curie FP6 RTN ENIGMA is acknowledge.
NO Dirección General de Enseñanza Superior e Investigación Científica
NO European Science Foundation: MISGAM
NO Marie Curie FP6 RTN
DS Docta Complutense
RD 26 abr 2025