On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries
Authors:
- Denis Blackmore,
- Yarema Prykarpatsky,
- Mykola M. Prytula,
- Denys Dutykh,
- Anatolij K. Prykarpatski
Abstract
There is studied the integrability of a generalized Gurevich-Zybin dynamical system based on the differential-algebraic and geometrically motivated gradient-holonomic approaches. There is constructed the corresponding Lax type represenation, compatible Poisson structures as well as the integrability of the related Hunter-Saxton reduction. In particular, there are constructed its Lax type repreentation, the Hamiltonian symmetries as flows on a functional manifold endowed with compatible Poisson structures as well as so called new mysterious symmetries, depending on functional parameter. Similar results are also presented for the potential-KdVdynamical system, for which we also obtained its new mysterious symmetries first presented in a clear, enough short and analytically readable form.
- Record ID
- CUTac52db465ddc4a65905e3993c5d29522
- Publication categories
- ;
- Author
- Journal series
- Analysis and Mathematical Physics, ISSN 1664-2368, e-ISSN 1664-235X
- Issue year
- 2022
- Vol
- 12
- No
- 2
- Pages
- [1-26]
- Article number
- 66
- Other elements of collation
- Bibliografia (na s.) - 23-26; Bibliografia (liczba pozycji) - 55; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 12, Iss. 2
- Keywords in English
- generalized Gurevich-Zybin dynamical system, reduced Hunter-Saxton dynamical system, differential-algebraic analysis, symmetry analysis, potential-Korteweg-de Vries dynamical system, conservation laws, Hamiltonian system, integrability, asymptotic analysis, mysterious symmetries
- ASJC Classification
- ; ;
- DOI
- DOI:10.1007/s13324-022-00662-0 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s13324-022-00662-0 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 100
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTac52db465ddc4a65905e3993c5d29522/
- URN
urn:pkr-prod:CUTac52db465ddc4a65905e3993c5d29522
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