Physica D: Nonlinear Phenomena ( IF 2.7 ) Pub Date : 2020-05-28 , DOI: 10.1016/j.physd.2020.132546 Stanislav Opanasenko , Alexander Bihlo , Roman O. Popovych , Artur Sergyeyev
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.
中文翻译:
等温无滑移漂移通量模型的广义对称性,守恒律和哈密顿结构
我们研究了模拟等温无滑移漂移通量的微分方程的流体动力型系统。利用系统部分耦合且子系统简化为(1 + 1)维Klein-Gordon方程的事实,我们详尽地描述了该系统的广义对称性,余对称性和局部守恒律。证明了在广义对称作用下的一组地方守恒定律由两个零阶守恒定律组成。从地方保护法的整个空间中选出了翻译不变性保护法的子空间。我们还找到了广泛的局部递归算子族和一个非局部递归算子,并构造了包含单个参数任意函数的哈密顿结构的无限族。对于每个构造的哈密顿算子,