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

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