Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Backlund transformations for Affine Toda Hierarchies   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.

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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph