G. S. Vasiliev, Jian-Gang Tang, B. Zh. Mamasoliev, “Invariant submodels of system equations of two-velocity hydrodynamics with equilibrium of pressure phases”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>585

Differentical equations, dynamical systems and optimal control

Invariant submodels of system equations of two-velocity hydrodynamics with equilibrium of pressure phases

G. S. Vasiliev^a, Jian-Gang Tang^b, B. Zh. Mamasoliev^c

^a Institute of Computational Mathematics and Mathematical Geophysics, pr. Lavrentieva, 6, 630090, Novosibirsk, Russia
^b YiLi Normal University, Jiefang Road, 448, 835000, Yinning Xinjiang, P.R. of China
^c National University of Uzbekistan named after Mirzo Ulugbek, Universitet Ko'chasi, 4, 100174, Tashkent, Uzbekistan

Abstract: We found the main core of Lie groups of transformations for a one-dimensional system of two-velocity hydrodynamic equations with equilibrium of pressure phases, using the theory of Lie groups and Lie algebra. Also, all systems of differential equations for invariant and partially invariant solutions for all non-subgroups, algebras that are included in optimal systems are written out. In some cases, solutions have been found.

Keywords: two-velocity hydrodynamic, Lie algebra, invariant solution.

UDC: 512.812.4

MSC: 17B81

Received June 17, 2016, published May 17, 2018

DOI: 10.17377/semi.2018.15.047