On the Complete Integrability of a One Generalized Riemann Type Hydrodynamic System
Denis Blackmore, Yarema A. Prykarpatsky, Orest D. Artemowych and, Anatoliy K. Prykarpatsky
TL;DR
This paper investigates the complete integrability of a generalized Riemann type hydrodynamic system using symplectic, algebraic, and Lax pair methods, establishing its rich mathematical structure.
Contribution
It introduces compatible Poisson structures, a Lax representation, and an infinite hierarchy of conservation laws for the system, demonstrating its integrability.
Findings
Existence of compatible polynomial Poisson structures
Construction of a Lax pair representation
Development of an infinite hierarchy of conservation laws
Abstract
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related infinite hierarchy of conservation laws are constructed.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems