A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

Anatolij M. Samoilenko; Yarema A. Prykarpatskyy; Denis Blackmore; Anatolij K. Prykarpatski

doi:10.18514/MMN.2018.2338

A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

Anatolij M. Samoilenko, Yarema A. Prykarpatskyy, Denis Blackmore, Anatolij K. Prykarpatski

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The complete integrability of a generalized Riemann type hydrodynamic hierarchy is studied by means of a novel combination of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, a Lax representation and a related infinite hierarchy of conservation laws are constructed. The current investigation provides an interesting glimpse of what is apparently a far wider range of applications.

Original language	English (US)
Pages (from-to)	555-567
Number of pages	13
Journal	Miskolc Mathematical Notes
Volume	19
Issue number	1
DOIs	https://doi.org/10.18514/MMN.2018.2338
State	Published - 2018

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Numerical Analysis
Discrete Mathematics and Combinatorics
Control and Optimization

Keywords

Bi- Hamiltonian structure
Conservation laws
Differential ideals
Lax type integrability
Lax-Noether equation
Poissonian structures
Riemann type hydrodynamic hierachy

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10.18514/MMN.2018.2338

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keywords = "Bi- Hamiltonian structure, Conservation laws, Differential ideals, Lax type integrability, Lax-Noether equation, Poissonian structures, Riemann type hydrodynamic hierachy",

author = "Samoilenko, {Anatolij M.} and Prykarpatskyy, {Yarema A.} and Denis Blackmore and Prykarpatski, {Anatolij K.}",

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AU - Prykarpatskyy, Yarema A.

AU - Blackmore, Denis

AU - Prykarpatski, Anatolij K.

PY - 2018

Y1 - 2018

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AB - The complete integrability of a generalized Riemann type hydrodynamic hierarchy is studied by means of a novel combination of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, a Lax representation and a related infinite hierarchy of conservation laws are constructed. The current investigation provides an interesting glimpse of what is apparently a far wider range of applications.

KW - Bi- Hamiltonian structure

KW - Conservation laws

KW - Differential ideals

KW - Lax type integrability

KW - Lax-Noether equation

KW - Poissonian structures

KW - Riemann type hydrodynamic hierachy

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ER -

A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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