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Recursion operators admitted by non-Abelian Burgers equations: some remarks
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Universit`a di Roma, 16, Via A. Scarpa, 00161 Rome, Italy.
Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Universit`a di Roma, 16, Via A. Scarpa, 00161 Rome, Italy.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
2017 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166Article in journal (Refereed) In press
Abstract [en]

The recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here considered. 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 rt=rxx+2rxrrt=rxx+2rxr. 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 rr 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.

Place, publisher, year, edition, pages
2017.
Keyword [en]
Recursion operator, Bäcklund transformations, Non-Abelian nonlinear evolution equations, Burgers equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-29469DOI: 10.1016/j.matcom.2017.02.001OAI: oai:DiVA.org:miun-29469DiVA: diva2:1052906
Note

Available online 24 February 2017

Available from: 2016-12-07 Created: 2016-12-07 Last updated: 2017-03-14Bibliographically approved

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Publisher's full texthttps://arxiv.org/pdf/1606.07270.pdf

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CiteExportLink to record
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