Deformations of the Poisson brackets and the Kowalevski top
Yu.A. Grigorev, A. V. Tsiganov
TL;DR
This paper investigates deformations of polynomial Poisson brackets related to the Kowalevski top, revealing new separation variables and a bi-Hamiltonian structure for an integrable deformation of the Kowalevski gyrostat.
Contribution
It introduces novel variables of separation and a bi-Hamiltonian framework for a deformed Kowalevski gyrostat, extending understanding of integrable systems.
Findings
New variables of separation from Yehia systems
Bi-Hamiltonian description of the deformed Kowalevski gyrostat
Enhanced understanding of polynomial Poisson pencil deformations
Abstract
Deformations of the known polynomial Poisson pencils associated with the Kowalevski top are studied. As a result we find new variables of separation from the one of the Yehia systems and new bi-Hamiltonian description of the integrable deformation of the Kowalevski gyrostat in two fields proposed by Sokolov and Tsiganov.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra