On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries
Document Type
Article
Publication Date
4-1-2022
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.
Identifier
85127511526 (Scopus)
Publication Title
Analysis and Mathematical Physics
External Full Text Location
https://doi.org/10.1007/s13324-022-00662-0
e-ISSN
1664235X
ISSN
16642368
Issue
2
Volume
12
Recommended Citation
Blackmore, Denis; Prykarpatsky, Yarema; Prytula, Mykola M.; Dutykh, Denys; and Prykarpatski, Anatolij K., "On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries" (2022). Faculty Publications. 3036.
https://digitalcommons.njit.edu/fac_pubs/3036