On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations

2012/11/19 by Raphael Boll, Boll, Raphael
Mathematics · Physics and Astronomy · #37K10 #37K35 #39A12 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:37K10 #msc:37K35 #msc:39A12 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1211.4374

33 pages, 23 figures

arxiv created 2013/05/29 · arxiv updated 2013/05/30

Abstract

We prove the Bianchi permutability (existence of superposition principle) of Bäcklund transformations for asymmetric quad-equations. Such equations and there Bäcklund transformations form 3D consistent systems of a priori different equations. We perform this proof by using 4D consistent systems of quad-equations, the structural insights through biquadratics patterns and the consideration of super-consistent eight-tuples of quad-equations on decorated cubes.

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