Bi-Hamiltonian ODEs with matrix variables

2011/05/09 by Alexander Odesskii, Odesskii, Alexander, Vladimir Rubtsov +3
Mathematics · Physics and Astronomy · #14H70 #17B63 #17B80 #32L81 #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1105.1740

openalex publication_date 2011/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets and found the corresponding hierarchy of integrable models, which generalizes the two-component Manakov's matrix system in the case of arbitrary number of matrices.

Citations

• On the Associative Analog of Lie Bialgebras

Related

• Poisson integrators
• Local bi-integrability of bi-Hamiltonian systems via bi-Poisson reduction
• Integrability of bi-Hamiltonian systems using Casimir functions and characteristic polynomials
• Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
• Multi-Hamiltonian formulation for a class of degenerate completely integrable systems