Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited

A differential-algebraic approach to studying the Lax integrability of the generalized Riemann type hydrodynamic hierarchy is revisited and its new Lax representation is constructed in exact form. The bi-Hamiltonian integrability of the generalized Riemann type hierarchy is discussed by means of the gradient-holonomic and symplectic methods and the related compatible Poissonian structures for N = 3 and N = 4 are constructed. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4761821]