Pfeiffer-Sato solutions of Buhl’s problem and a Lagrange-D’Alembert principle for heavenly equations
Authors:
- Oksana E. Hentosh,
- Yarema A. Prykarpatsky,
- Denis Blackmore,
- Anatolij Prykarpatski
Abstract
This review is devoted to the Buhl compatible vector eld equation problem, emphasizing its Pfei er and Lax{Sato type solutions. We analyze the related Lie-algebraic structures and integrability of the heavenly equations. AKS-algebraic and related R-structure schemes are used to study the corresponding co-adjoint actions. Their compatibility conditions are shown to coincide with the corresponding heavenly equations, all of which originate in this way and can be represented as a Lax compatibility condition. The in nite hierarchy of conservation laws for the heavenly equations is described along with its Casimir invariant connection and several examples are presented. An interesting related Lagrange{d'Alembert principle is also discussed. A generalization of the scheme, related to the loop Lie superalgebra of the Lie super group of superconformal di eomorphisms of the 1jN-dimensional supertorus, is used to construct Lax{Sato integrable supersymmetric analogs of the Mikhalev{Pavlov heavenly equation for every N 2 Nnf4; 5g. Super-analogs of Liouville equations are constructed using superconformal maps.
- Record ID
- CUT11fcfd2f53af40dc9bb737b55e7bbc21
- Publication type
- Publication categories
- ; ;
- Author
- Pages
- 187-233
- Other elements of collation
- rys.; Bibliografia (na s.) - 225-233; Bibliografia (liczba pozycji) - 97; Oznaczenie streszczenia - Abstr.
- Book
- Euler Norbert Norbert Euler (eds.): Nonlinear systems and their remarkable mathematical structures. Vol. 1, 2019, Boca Raton, Taylor & Francis Group, CRC Press Taylor & Francis Group, ISBN 978-1-1386-0100-0
- Keywords in English
- Pfeiffer-Sato integrability, nonlinear dynamical systems
- URL
- https://www.taylorfrancis.com/books/9781138601000 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 50
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT11fcfd2f53af40dc9bb737b55e7bbc21/
- URN
urn:pkr-prod:CUT11fcfd2f53af40dc9bb737b55e7bbc21
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