2019/08/31 by Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych +1
Mathematics · Physics and Astronomy · #Classical mechanics #Conservation law #Conserved quantity #Geometry #Hamiltonian (control theory) #Homogeneous space #Law #Mathematical analysis #Mathematical physics #Mathematics #Noether's theorem #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Quantum chaos and dynamical systems #math-ph #math.AP #math.MP #msc:35B06 #msc:37K05 #msc:76M60 #nlin.SI
paper · pdf · doi:10.1016/j.physd.2020.132546
published as Phys. D 411 (2020), 132546, 19 pp · 36 pages, extended version, the proof on cosymmetries in presented with more details
openalex publication_date 2020/05/27 · arxiv created 2020/06/20 · arxiv updated 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.