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On the Whitham hierarchy: dressing scheme, string equations and additional symmetries

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Mañas Baena, Manuel and Medina, Elena and Martínez Alonso, Luis (2006) On the Whitham hierarchy: dressing scheme, string equations and additional symmetries. Journal of physics A: Mathematical and general, 39 (10). pp. 2349-2381. ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/39/10/008




Abstract

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.


Item Type:Article
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©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.

Uncontrolled Keywords:Dispersionless Kp hierarchy; Toda hierarchy; Integrable hierarchies; Tau-function; Hodograph solutions; Benney equations; Conformal-maps; Reductions; Growth; Limit
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32552
Deposited On:27 Jul 2015 10:00
Last Modified:10 Dec 2018 15:09

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