Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I
Authors:
- O. E. Hentosh,
- Ya. A. Prykarpatskyy,
- A. A. Balinsky,
- A. K. Prykarpatski
Abstract
We present a review of differential-geometric and Lie-algebraic approaches to the investigation of a broad class of nonlinear integrable differential systems of “heavenly” type associated with Hamiltonian flows on the spaces conjugate to the loop Lie algebras of vector fields on the tori. These flows are generated by the corresponding orbits of the coadjoint action of loop diffeomorphism groups and satisfy the Lax–Satotype vector-field compatibility conditions. We analyze the corresponding hierarchies of conservation laws and their relationships with Casimir invariants. We consider typical examples of these systems and establish their complete integrability by using the developed Lie-algebraic construction. We also describe new generalizations of the integrable dispersion-free systems of heavenly type for which the corresponding generating elements of the orbits have factorized structures, which allows their extension to the multidimensional case.
- Record ID
- CUTe21497d4598f4c318005cea7fb804da8
- Publication categories
- ;
- Author
- Journal series
- Ukrainian Mathematical Journal, ISSN 0041-5995, e-ISSN 1573-9376
- Issue year
- 2023
- Vol
- 74
- No
- 8
- Pages
- 1175-1208
- Other elements of collation
- Bibliografia (na s.) - 1206-1208; Bibliografia (liczba pozycji) - 72; Oznaczenie streszczenia - Streszcz. ang.; Numeracja w czasopiśmie - Vol. 74, No. 8
- Substantive notes
- Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 8, pp. 1029–1059, August, 2022. Ukrainian DOI: 10.37863/ umzh.v74i8.6614.
- Keywords in English
- geometric structure, loop diffeomorphism groups, heavenly-type Hamiltonian systems, integrability
- ASJC Classification
- DOI
- DOI:10.1007/s11253-023-02129-2 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s11253-023-02129-2 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 40
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTe21497d4598f4c318005cea7fb804da8/
- URN
urn:pkr-prod:CUTe21497d4598f4c318005cea7fb804da8
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