Abelian versus non-Abelian BÄcklund charts : Some remarks


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Publication Details

Author list: Schiebold, Cornelia

Publication year: 2019

Start page: 43

End page: 55

Number of pages: 13

ISSN: 2163-2472

DOI: http://dx.doi.org/10.3934/eect.2019003


Connections via Bäcklund transformations among different nonlinear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via Bäcklund transformations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities between Bäcklund charts in the case of the Burgers-heat equation, on one side, and KdV-type equations, on the other, are considered. The Bäcklund charts constructed in [16] and [17], respectively, to connect Burgers and KdV-type hierarchies of operator nonlinear evolution equations show that the structures, in the non-commutative cases, are richer than the corresponding commutative ones.


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