On the r-th dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions



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Mañas Baena, Manuel (2004) On the r-th dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions. Journal of physics A: Mathematical and general, 37 (39). pp. 9195-9224. ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/37/39/010


For a family of Poisson algebras, parametrized by r is an element of Z, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context, we rederive the recently found rth dispersionless modified KP hierarchies and rth dispersionless Dym hierarchies, giving a new Miura map among them. We also found a new integrable hierarchy which we call the rth dispersionless Toda hierarchy. Moreover, additional symmetries for these hierarchies are studied in detail and new symmetries depending on arbitrary functions are explicitly constructed for the rth dispersionless KP, rth dispersionless Dym and rth dispersionless Toda equations. Some solutions are derived by examining the imposition of a time invariance to the potential rth dispersionless Dym equation, for which a complete integral is presented and, therefore, an appropriate envelope leads to a general solution. Symmetries and Miura maps are applied to get new solutions and solutions of the rth dispersionless modified KP equation.

Item Type:Article
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©IOP Publishing.
The author thanks Luis Martínez Alonso and Elena Medina for several discussions. Partial economical support from Dirección General de Enseñanza Superior e Investigación Científica no. BFM2002-01607 is also acknowledged.

Uncontrolled Keywords:Topological field-theory; Classical R-matrices; Integrable hierarchies; Kp hierarchy; Whitham hierarchy; Poisson algebras; Conformal-maps; Lax equations; Dkp equation; Tau-function
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32559
Deposited On:27 Jul 2015 11:19
Last Modified:10 Dec 2018 15:09

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