Gauge symmetry origin of Bäcklund transformations for Painlevé equations

We identify the self-similarity limit of the second flow of sl ( N ) mKdV hierarchy with the periodic dressing chain thus establishing a connection to A N − 1 ( 1 ) invariant Painlevé equations. The A N − 1 ( 1 ) Bäcklund symmetries of dressing equations and Painlevé equations are obtained in the se...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-05, Vol.54 (19), p.195701
Main Authors: Alves, V C C, Aratyn, H, Gomes, J F, Zimerman, A H
Format: Article
Language:English
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Summary:We identify the self-similarity limit of the second flow of sl ( N ) mKdV hierarchy with the periodic dressing chain thus establishing a connection to A N − 1 ( 1 ) invariant Painlevé equations. The A N − 1 ( 1 ) Bäcklund symmetries of dressing equations and Painlevé equations are obtained in the self-similarity limit of gauge transformations of the mKdV hierarchy realized as zero-curvature equations on the loop algebra s l ̂ ( N ) endowed with a principal gradation.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/abf2ee