2026-06-27T16:26:36Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/515352024-08-26T17:25:48Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Mañas Baena, Manuel Enrique
2023-06-20T10:58:21Z
2023-06-20T10:58:21Z
2004-08-01
0305-4470
https://hdl.handle.net/20.500.14352/51535
http://dx.doi.org/10.1088/0305-4470/37/39/010
http://iopscience.iop.orghttp://arxiv.org/abs/nlin/0404022
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.
eng
On the r-th dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions
journal article
URL
https://docta.ucm.es/bitstreams/eea214e4-7064-4621-8f4b-a9728ae7ff96/download
File
MD5
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application/pdf
mañas14preprint.pdf
URL
https://docta.ucm.es/bitstreams/4018b9e4-f21a-43ab-8fc8-d07c1bc499ed/download
File
MD5
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text/plain
mañas14preprint.pdf.txt