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arXiv · 1606.07270

Recursion Operators admitted by non-Abelian Burgers equations: Some Remarks

Sandra Carillo·Mauro Lo Schiavo·Cornelia Schiebold
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Abstract

The recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here con- sidered. Specifically, evolution equations wherein the unknown is an operator acting on a Banach space are investigated. Here, the mirror non-Abelian Burgers equation is considered: it can be written as $r_t = r_{xx} + 2r_x r$. The structural properties of the admitted recursion operator are studied; thus, it is proved to be a strong symmetry for the mirror non-Abelian Burgers equation as well as to be the hereditary. These results are proved via direct computations as well as via computer assisted manipulations; ad hoc routines are needed to treat non-Abelian quantities and relations among them. The obtained recursion operator generates the $mirror$ non-Abelian Burgers hierarchy. The latter, when the unknown operator $r$ is replaced by a real valued function reduces to the usual (commutative) Burgers hierarchy. Accordingly, also the recursion operator reduces to the usual Burgers one.

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Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold. 2016-06-23. Recursion Operators admitted by non-Abelian Burgers equations: Some Remarks. https://doi.org/10.1016/j.matcom.2017.02.001

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