Generalized Backlund transformations for Affine Toda Hierarchies

Abstract

The construction of generalized Backlund transformation for the $A_n$ 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 Backlund transformations. Moreover, explicit examples for $su(3)$ and $su(4)$ lead to uncover interesting composition properties of various types of Backlund transformations. The universality character of the gauge-Backlund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Backlund transformations to higher flow equations. Explicit example for the simplest higher flow of the $sl(3)$ hierarchy is presented.

arXiv comment23 pages, Latex

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Cited by in corpus (5)

• Gauge Miura and Backlund Transformations for Generalized $A_n$-KdV Hierarchies
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• Twisted Affine Integrable Hierarchies and Soliton Solutions
• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies