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

PHYSICA D-NONLINEAR PHENOMENA

卷:411

Article

Opanasenko, Stanislav^1,2  Bihlo, Alexander¹  Popovych, Roman O.^2,3,4  Sergyeyev, Artur⁴ 

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] NAS Ukraine, Inst Math, 3 Tereshchenkivska Str, UA-01024 Kiev, Ukraine

[3] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[4] Silesian Univ Opava, Math Inst, Rybnicku 1, Opava 74601, Czech Republic

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

DOI  :  10.1016/j.physd.2020.132546

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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