Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type

DOI10.1016/j.chaos.2013.11.012zbMath1348.37101OpenAlexW2031812012MaRDI QIDQ339513

Yarema A. Prykarpatsky, Nikolai N. jun. Bogoliubov, D. L. Blackmore, Anatoliy K. Prykarpatsky

Publication date: 11 November 2016

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2013.11.012

zbMATH Keywords

bi-Hamiltonian integrabilityinfinite hierarchy of conservation lawsLax integrabilityRiemann type hydrodynamic hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (6)

Integrability analysis of a two-component Burgers-type hierarchy ⋮ New Dubrovin-type integrability theory applications of differential rings ⋮ Dark Equations and Their Light Integrability ⋮ Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems ⋮ The Cauchy problem for a generalized Riemann-type hydrodynamical equation ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators

Cites Work

• The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamic systems
• The matrix Lax representation of the generalized Riemann equations and its conservation laws
• On a nonlocal Ostrovsky-Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Extension of the module of invertible transformations. Classification of integrable systems
• Infinte Lie-Bäcklund algebras
• A Lie algebra structure in a formal variational calculation
• The calculus of jets and nonlinear Hamiltonian systems
• The resolvent and Hamiltonian systems
• Finite dimensional local and nonlocal reductions of one type of hydrodynamic systems
• On the geometry of soliton equations
• Classification of integrable polynomial vector evolution equations
• Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited
• Integrability of the modified generalised Vakhnenko equation
• Picard-Vessiot Extensions of Real Differential Fields
• The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations
• The gradient-holonomic integrability analysis of a Whitham-type nonlinear dynamical model for a relaxing medium with spatial memory
• Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg–de Vries hydrodynamical equations
• The Hunter–Saxton equation: remarkable structures of symmetries and conserved densities
• The Hamiltonian structure of a complex version of the Burgers hierarchy
• The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• Solitons in a nonlinear model medium
• Almost Periodic Solutions of the KdV Equation
• A simple model of the integrable Hamiltonian equation
• The stability of solutions of Vakhnenko's equation
• Hamiltonian formulation of odd Burgers hierarchy
• The Gurevich–Zybin system
• On an integrable hierarchy derived from the isentropic gas dynamics
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
• On the quasi-Hamiltonian formalism of the KdV equation
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