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arXiv · 2101.05859

Gauge Symmetry Origin of B\"acklund Transformations for Painlev\'e Equations

V. C. C. Alves·H. Aratyn·J. F. Gomes·A. H. Zimerman
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Abstract

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 $A^{(1)}_{N-1}$ invariant Painlev\'e equations. The $A^{(1)}_{N-1}$ B\"acklund symmetries of dressing equations and Painlev\'e equations are obtained in the self-similarity limit of gauge transformations of the mKdV hierarchy realized as zero-curvature equations on the loop algebra $\widehat{sl}(N)$ endowed with a principal gradation.

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V. C. C. Alves, H. Aratyn, J. F. Gomes, A. H. Zimerman. 2021-01-14. Gauge Symmetry Origin of B\"acklund Transformations for Painlev\'e Equations. https://doi.org/10.1088/1751-8121%2Fabf2ee

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