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

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Physica D: Nonlinear Phenomena

RIV identification code

RIV/47813059:19610/20:A0000068

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1016/j.physd.2020.132546

UT WoS

000558454900017

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.

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

Abstract

V originále

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.

Citovat

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://dx.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 = {http://dx.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://dx.doi.org/10.1016/j.physd.2020.132546.

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