DARBOUXTYPE OPERATORS FOR ONEDIMENSIONAL GAS DYNAMICS
V.E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc 1993. Вып.1. С. 3843.
The linear differential operator la found that generalizes the operator called Darboux operator by the author which is well known in onedimensional polytropic gas flow theory. The operator found relates linear equations obtained from equations of onedimensional plane isentropic gas dynamics written in Eulerian and Lagrangian variables in the case of arbitrary equation of state using Legendre transformation. The problem of existence of a similar operator is solved for a special class of second order linear equations being natural generalization of linearized onedimensional gas dynamics equations. The existence of all these operators is shown to be provided by the corresponding equations invariance with respect to transformations analogous to Galilean transfer.
