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Abelian versus non-Abelian Bäcklund charts: Some remarks
Università di Roma La Sapienza, Scarpa, Italy; I.N.F.N.-Sez. Roma1, Gr.IV: Mathematical Methods in NonLinear Physics Rome, Italy.
Università di Roma La Sapienza, Rome, Italy.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
2019 (English)In: Evolution Equations and Control Theory, ISSN 2163-2472, Vol. 8, no 1, p. 43-55Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
2019. Vol. 8, no 1, p. 43-55
Keywords [en]
Burgers equations, Bäcklund transformations, Cole-Hopf Transformations, Invariances, Korteweg deVries-type equations, Nonlinear evolution equations, Recursion operators
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-35834DOI: 10.3934/eect.2019003ISI: 000462022800004Scopus ID: 2-s2.0-85061866201OAI: oai:DiVA.org:miun-35834DiVA, id: diva2:1297495
Available from: 2019-03-20 Created: 2019-03-20 Last updated: 2019-05-20Bibliographically approved

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Schiebold, Cornelia

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CiteExportLink to record
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