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 invariant Painlev equations. The Bcklund symmetries of dressing equations and Painlev equations are obtained in the self-similarity limit of gauge transformations of the mKdV hierarchy realized as zero-curvature equations on the loop algebra endowed with a principal gradation.

中文翻译：

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Painlev 方程 Bcklund 变换的规范对称原点

我们用周期性修整链确定了sl ( N ) mKdV 层次结构的第二个流的自相似性极限，从而建立了与不变 Painlev 方程的连接。修整方程和 Painlev 方程的Bcklund 对称性是在 mKdV 层次规范变换的自相似极限中获得的，实现为具有主阶阶的环代数上的零曲率方程。