The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

TL;DR

This paper revisits the integrability of the Riemann type hierarchy using differential-algebraic methods, presenting new Lax representations and Poisson structures, and exploring its bi-Hamiltonian properties.

Contribution

It introduces new Lax type representations and Poisson structures for the Riemann hierarchy, advancing the understanding of its integrability properties.

Findings

New Lax type representation constructed

Poisson structures explicitly formulated

Bi-Hamiltonian integrability discussed

Abstract

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.