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

Access to Document

10.18514/MMN.2018.2338

Cite this

@article{43222d0ada3841989b1b45a26aaf4e5a,

title = "A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy",

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.",

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.}",

note = "Publisher Copyright: {\textcopyright} 2018 Miskolc University Press.",

year = "2018",

doi = "10.18514/MMN.2018.2338",

language = "English (US)",

volume = "19",

pages = "555--567",

journal = "Miskolc Mathematical Notes",

issn = "1787-2405",

publisher = "University of Miskolc",

number = "1",

}

TY - JOUR

T1 - A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

AU - Samoilenko, Anatolij M.

AU - Prykarpatskyy, Yarema A.

AU - Blackmore, Denis

AU - Prykarpatski, Anatolij K.

PY - 2018

Y1 - 2018

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85049135448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049135448&partnerID=8YFLogxK

U2 - 10.18514/MMN.2018.2338

DO - 10.18514/MMN.2018.2338

M3 - Article

AN - SCOPUS:85049135448

SN - 1787-2405

VL - 19

SP - 555

EP - 567

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

IS - 1

ER -

A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this