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...

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Bibliographic Details
Published in:Journal of mathematical physics 2012-10, Vol.53 (10)
Main Authors: Prykarpatsky, Yarema A., Artemovych, Orest D., Pavlov, Maxim V., Prykarpatsky, Anatoliy K.
Format: Article
Language:English
Subjects:
Compatibility
Computational fluid dynamics
Construction
Fluid flow
Hierarchies
Hydrodynamics
Mathematical analysis
Representations
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4761821