Generalized symmetries, conservation laws and Hamiltonian
structures of an isothermal no-slip drift flux model

J 2020

Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model

OPANASENKO, Stanislav; Alexander BIHLO; Roman POPOVYCH and Artur SERGYEYEV

Basic information

Original name

Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model

Authors

OPANASENKO, Stanislav (804 Ukraine, guarantor); Alexander BIHLO (40 Austria); Roman POPOVYCH (804 Ukraine, belonging to the institution) and Artur SERGYEYEV (804 Ukraine, belonging to the institution)

Edition

Physica D: Nonlinear Phenomena, Amsterdam, Elsevier B.V. 2020, 0167-2789

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

is not subject to a state or trade secret

References:

Physica D: Nonlinear Phenomena

Impact factor

Impact factor: 2.300

RIV identification code

RIV/47813059:19610/20:A0000068

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1016/j.physd.2020.132546

UT WoS

000558454900017

EID Scopus

2-s2.0-85086077115

Keywords in English

Generalized symmetry; Local conservation law; Recursion operator; Hamiltonian structure; Hydrodynamic-type system; Isothermal no-slip drift flux

Links

GBP201/12/G028, research and development project.

Changed: 6/4/2021 13:40, Mgr. Aleš Ryšavý

Abstract

In the original language

We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduces to the (1+1)-dimensional Klein-Gordon equation, we exhaustively describe generalized symmetries, cosymmetries and local conservation laws of this system. A generating set of local conservation laws under the action of generalized symmetries is proved to consist of two zeroth-order conservation laws. The subspace of translation-invariant conservation laws is singled out from the entire space of local conservation laws. We also find broad families of local recursion operators and a nonlocal recursion operator, and construct an infinite family of Hamiltonian structures involving an arbitrary function of a single argument. For each of the constructed Hamiltonian operators, we obtain the associated algebra of Hamiltonian symmetries.

Cite

OPANASENKO, Stanislav; Alexander BIHLO; Roman POPOVYCH and Artur SERGYEYEV. Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model. Physica D: Nonlinear Phenomena. Amsterdam: Elsevier B.V., 2020, vol. 411, No 132546, p. "132546-1"-"132546-19", 19 pp. ISSN 0167-2789. Available from: https://doi.org/10.1016/j.physd.2020.132546.

@article{49264,
   author = {Opanasenko, Stanislav and Bihlo, Alexander and Popovych, Roman and Sergyeyev, Artur},
   article_location = {Amsterdam},
   article_number = {132546},
   doi = {https://doi.org/10.1016/j.physd.2020.132546},
   keywords = {Generalized symmetry; Local conservation law; Recursion operator; Hamiltonian structure; Hydrodynamic-type system; Isothermal no-slip drift flux},
   language = {eng},
   issn = {0167-2789},
   journal = {Physica D: Nonlinear Phenomena},
   title = {Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model},
   url = {https://www.sciencedirect.com/science/article/pii/S0167278920300506?via%3Dihub},
   volume = {411},
   year = {2020}
}

TY  - JOUR
ID  - 49264
AU  - Opanasenko, Stanislav - Bihlo, Alexander - Popovych, Roman - Sergyeyev, Artur
PY  - 2020
TI  - Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
JF  - Physica D: Nonlinear Phenomena
VL  - 411
IS  - 132546
SP  - "132546-1"-"132546-19"
EP  - "132546-1"-"132546-19"
PB  - Elsevier B.V.
SN  - 01672789
KW  - Generalized symmetry
KW  - Local conservation law
KW  - Recursion operator
KW  - Hamiltonian structure
KW  - Hydrodynamic-type system
KW  - Isothermal no-slip drift flux
UR  - https://www.sciencedirect.com/science/article/pii/S0167278920300506?via%3Dihub
N2  - We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduces to the (1+1)-dimensional Klein-Gordon equation, we exhaustively describe generalized symmetries, cosymmetries and local conservation laws of this system. A generating set of local conservation laws under the action of generalized symmetries is proved to consist of two zeroth-order conservation laws. The subspace of translation-invariant conservation laws is singled out from the entire space of local conservation laws. We also find broad families of local recursion operators and a nonlocal recursion operator, and construct an infinite family of Hamiltonian structures involving an arbitrary function of a single argument. For each of the constructed Hamiltonian operators, we obtain the associated algebra of Hamiltonian symmetries.
ER  -

OPANASENKO, Stanislav; Alexander BIHLO; Roman POPOVYCH and Artur SERGYEYEV. Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model. \textit{Physica D: Nonlinear Phenomena}. Amsterdam: Elsevier B.V., 2020, vol.~411, No~132546, p.~''132546-1''-''132546-19'', 19 pp. ISSN~0167-2789. Available from: https://doi.org/10.1016/j.physd.2020.132546.

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