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On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-0370-7274
2019 (English)In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 143, no 2, p. 139-156Article in journal (Refereed) Published
Abstract [en]

We consider symmetry‐integrable evolution equations in 1 + 1 dimensions of order 3 and order 5. We show that there exist only three equations in this class that are invariant under the Möbius transformation, and we name those Schwarzian equations. We report an interesting relation between the recursion operators of the Schwarzian equations and the corresponding adjoint operators that generate hierarchies of Schwarzian systems in terms of the Schwarzian derivative. This indicates a deep relation between the Schwarzian equations and the Schwarzian derivative. A classification of the fully nonlinear third‐order Schwarzian equations is also reported.

Place, publisher, year, edition, pages
John Wiley & Sons, 2019. Vol. 143, no 2, p. 139-156
Keywords [en]
dynamical systems, mathematical physics, partial differential equations
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-74953DOI: 10.1111/sapm.12268ISI: 000476678700002Scopus ID: 2-s2.0-85065337676OAI: oai:DiVA.org:ltu-74953DiVA, id: diva2:1330039
Note

Validerad;2019;Nivå 2;2019-08-06 (johcin)

Available from: 2019-06-25 Created: 2019-06-25 Last updated: 2019-08-06Bibliographically approved

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Euler, MariannaEuler, Norbert

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