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DARBOUX-TYPE OPERATORS FOR ONE-DIMENSIONAL GAS DYNAMICS

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc 1993. Вып.1. С. 38-43.

      The linear differential operator la found that generalizes the operator called Darboux operator by the author which is well known in one-dimensional polytropic gas flow theory. The operator found relates linear equations obtained from equations of one-dimensional 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 one-dimensional 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.










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