The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure
Authors:
- Oksana E. Hentosh,
- Yarema A. Prykarpatsky,
- Alexandr Balinsky,
- Anatolij K. Prykarpatski
Abstract
There are reviewed modern investigations devoted to studying nonlinear dispersiveless heavenly type integrable evolutions systems on functional spaces within the modern differential-geometric and algebraic tools. Main accent is done on the loop diffeomorphism group vector fi elds on the complexifi ed torus and the related Lie-algebraic structures, generating dispersionless heavenly type integrable systems. As examples, we analyzed the Einstein–Weyl metric equation, the modifi ed Einstein–Weyl metric equation, the Dunajski heavenly equation system, the fi rst and second conformal structure generating equations, the inverse fi rst Shabat reduction heavenly equation, the fi rst and modifi ed Plebański heavenly equations, the Husain heavenly equation, the general Monge equation and the classical Korteweg-de Vries dispersive dynamical system. We also investigated geometric structures of a class of spatially one-dimensional completely integrable Chaplygin type hydrodynamic systems, which proved to be deeply connected with differential systems on the complexifi ed torus and the related diffeomorphism group orbits on them.
- Record ID
- CUT7ad420dfd1a94335822ac5462a3640e3
- Publication categories
- ; ;
- Author
- Journal series
- Annals of Mathematics and Physics, ISSN 2689-7636
- Issue year
- 2019
- Vol
- 2
- No
- 1
- Pages
- [1-15]
- Other elements of collation
- Bibliografia (na s.) - 14-15; Bibliografia (liczba pozycji) - 35; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 2, Iss. 1
- Keywords in English
- Hamiltonian systems
- DOI
- DOI:10.17352/amp.000006 Opening in a new tab
- URL
- https://www.peertechz.com/journals/annals-of-mathematics-and-physics/archive Opening in a new tab
- Related project
- Teoria równań i nierówności różniczkowych, układy dynamiczne na rozmaitościach, wybrane działy: analizy matematycznej topologii algebry i geometrii oraz probabilistyki teorii grafów i liczb. . Project leader at PK: , ,
Działalność statutowa - Language
- eng (en) English
- License
- Score (nominal)
- 5
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT7ad420dfd1a94335822ac5462a3640e3/
- URN
urn:pkr-prod:CUT7ad420dfd1a94335822ac5462a3640e3
* 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.