An integrable family of Poisson systems: Characterization and global analysis

TL;DR

This paper investigates an n-dimensional family of solutions to the Jacobi PDEs, demonstrating their role in defining globally analyzable integrable Poisson systems that include various applied examples.

Contribution

It characterizes a broad family of Poisson structures that are globally analyzable and lead to integrable systems, extending beyond local Darboux theorem limitations.

Findings

The family of solutions is n-dimensional and of arbitrary nonlinearity.

These Poisson structures are shown to produce integrable systems.

The family includes several applied-interest systems as special cases.

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.