Invariance of the Equations of the Theory of Penetration with Respect to Galileo's Algebra and its Extensions - Ichanska, Nataliia; Serova, Maria; Skliarenko, Taras (International Journal of Engineering and Technology, 2018)
In this work, the symmetry properties of the system of equations of the theory of penetration, which describes the adiabatic motion of an inviscid compressible fluid, are investigated. Maximal invariance algebras of a class of systems that describe the adiabatic motion of an inviscid compressible fluid in the absence of mass forces and in their presence are found. The paper shows that for a given system one can observe a similar effect of the absence and presence of axial symmetry the same as for the known equations of mathematical physics, for example, the SchrÃ¶dinger equation. It was established that in the absence of axial symmetry, this system is invariant with respect to the generalized Galilean algebra AG2 (1, n) with a fixed power nonlinearity, and in the presence of axial symmetry the system is invariant with respect to the generalized Galilean algebra AG2 (1, n-1) with arbitrary power nonlinearity.Â