TY - JOUR
T1 - On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries
AU - Blackmore, Denis
AU - Prykarpatsky, Yarema
AU - Prytula, Mykola M.
AU - Dutykh, Denys
AU - Prykarpatski, Anatolij K.
N1 - Funding Information:
The authors are indebted to our colleagues Alexander Balinsky and Radoslaw Kycia with whom discussions during preparation of the manuscript were very useful. The last but not least appreciation belongs to Referee for important suggestions and remarks which proved very instrumental when preparing a manuscript.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/4
Y1 - 2022/4
N2 - 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.
AB - 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.
KW - Asymptotic analysis
KW - Compatible Poisson structures
KW - Conservation laws
KW - Differential-algebraic analysis
KW - Generalized Gurevich-Zybin dynamical system
KW - Hamiltonian system
KW - Integrability
KW - Mysterious symmetries
KW - Potential-Korteweg-de Vries dynamical system
KW - Reduced Hunter-Saxton dynamical system
KW - Symmetry analysis
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U2 - 10.1007/s13324-022-00662-0
DO - 10.1007/s13324-022-00662-0
M3 - Article
AN - SCOPUS:85127511526
SN - 1664-2368
VL - 12
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 2
M1 - 66
ER -