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Mañas Baena, Manuel (2004) On the rth dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions. Journal of physics A: Mathematical and general, 37 (39). pp. 91959224. ISSN 03054470

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Official URL: http://dx.doi.org/10.1088/03054470/37/39/010
URL  URL Type 

http://iopscience.iop.org  Publisher 
http://arxiv.org/abs/nlin/0404022  Organisation 
Abstract
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 

Additional Information:  ©IOP Publishing. 
Uncontrolled Keywords:  Topological fieldtheory; Classical Rmatrices; Integrable hierarchies; Kp hierarchy; Whitham hierarchy; Poisson algebras; Conformalmaps; Lax equations; Dkp equation; Taufunction 
Subjects:  Sciences > Physics > PhysicsMathematical 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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