The generalized centrally extended Lie algebraic structures and related integrable heavenly type equations
Authors:
- O. Ye. Hentosh,
- A. A. Balinsky,
- A. K. Prykarpatski
Abstract
There are studied Lie-algebraic structures of a wide class of heavenly type non-linear integrableequations, related with coadjoint flows on the adjoint spaceto a loop vector field Lie algebra onthe torus. These flows are generated by the loop Lie algebras of vector fields on a torus and theircoadjoint orbits and give rise to the compatible Lax-Sato type vector field relationships. The re-lated infinite hierarchy of conservations laws is analysed and its analytical structure, connectedwith the Casimir invariants, is discussed. We present the typical examples of such equations anddemonstrate in details their integrability within the scheme developed. As examples, we foundand described new multidimensional generalizations of theMikhalev-Pavlov and Alonso-Shabattype integrable dispersionless equation, whose seed elements possess a special factorized structure,allowing to extend them to the multidimensional case of arbitrary dimension.
- Record ID
- CUT045738efcad94011a3f93745cc562dd2
- Publication categories
- ;
- Author
- Journal series
- Carpathian Mathematical Publications, ISSN 2075-9827, e-ISSN 2313-0210
- Issue year
- 2020
- Vol
- 12
- No
- 1
- Pages
- 242-264
- Other elements of collation
- Bibliografia (na s.) - 261-264; Bibliografia (liczba pozycji) - 57; Oznaczenie streszczenia - Streszcz. ang., ukr.; Numeracja w czasopiśmie - Vol. 12, No. 1
- Keywords in English
- heavenly type equations, Lax integrability, Hamiltonian system, torus diffeomorphisms, loop Lie algebra, central extension, Lie-algebraic scheme, Casimir invariants, Lie-Poisson structure, R-structure, Mikhalev-Pavlov equations
- DOI
- DOI:10.15330/cmp.12.1.242-264 Opening in a new tab
- URL
- https://journals.pnu.edu.ua/index.php/cmp/issue/view/223 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT045738efcad94011a3f93745cc562dd2/
- URN
urn:pkr-prod:CUT045738efcad94011a3f93745cc562dd2
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.