On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries

Denis Blackmore, Yarema Prykarpatsky, Mykola M. Prytula, Denys Dutykh, Anatolij K. Prykarpatski

Research output: Contribution to journalArticlepeer-review

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.

Original languageBritish English
Article number66
JournalAnalysis and Mathematical Physics
Volume12
Issue number2
DOIs
StatePublished - Apr 2022

Keywords

  • Asymptotic analysis
  • Compatible Poisson structures
  • Conservation laws
  • Differential-algebraic analysis
  • Generalized Gurevich-Zybin dynamical system
  • Hamiltonian system
  • Integrability
  • Mysterious symmetries
  • Potential-Korteweg-de Vries dynamical system
  • Reduced Hunter-Saxton dynamical system
  • Symmetry analysis

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