An integrable family of Poisson systems: Characterization and global analysis

Abstract

A family of solutions of the Jacobi PDEs is investigated. This family is $n$-dimensional, of arbitrary nonlinearity and can be globally analyzed (thus improving the usual local scope of Darboux theorem). As an outcome of this analysis it is demonstrated that such Poisson structures lead to integrable systems. The solution family embraces as particular cases different systems of applied interest that are also regarded as examples.

arXiv admin note: substantial text overlap with arXiv:1910.06765, arXiv:1910.05141

References in corpus (2)

• Separation of variables in the Jacobi identities
• New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis

Cited by in corpus (5)

• Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces
• Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
• Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems
• New global solutions of the Jacobi partial differential equations
• Congruence method for global Darboux reduction of finite-dimensional Poisson systems