Generalized Bäcklund transformations for affine Toda hierarchies

The construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of g...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-02, Vol.54 (6), p.65202
Main Authors: de Carvalho Ferreira, J M, Gomes, J F, Lobo, G V, Zimerman, A H
Format: Article
Language:English
Subjects:
Backlund transformation
integrable hierarchies
solitons
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Summary:The construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Bäcklund transformations. Moreover, explicit examples for sl(3) and sl(4) lead to uncover interesting composition properties of various types of Bäcklund transformations. The universality character of the gauge-Bäcklund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Bäcklund transformations to higher flow equations. Explicit example for the simplest higher flow of the sl(3) hierarchy is presented.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/abd8b2