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arXiv · 1810.01862

Abelian versus non-Abelian Baecklund Charts: some remarks

Sandra Carillo·Mauro Lo Schiavo·Cornelia Schiebold
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Abstract

Connections via Baecklund transformations among different non-linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via Baecklund transformations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities between Baecklund charts in the case of the Burgers - heat equation, on one side and KdV -type equations are considered. The Baecklund 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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Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold. 2018-10-03. Abelian versus non-Abelian Baecklund Charts: some remarks. https://doi.org/10.3934/eect.2019003

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