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A FUNDAMETAL SYSTEM OF SOLUTIONS TO THE EQUATION OF ONE-DIMENSIONAL PLANE ISENTROPIC FLOWS OF A POLYTROPIC GAS

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Rroc 1990. Вып.1. С. 35-40.

      The velocity potential equation describing one-dimensional plane isentropic flows of a polytropic gas is linearized using the classic Legendre transformation (hodograph). For the linear equation in the hodograph variables, a fundamental system of uniform polynomial solutions has been found, which is used for the global solution of Cauchy problem in the hodograph plane. A general method of constructing explicit formulas representing the polynomial solution factors via binomial factors is given. Recursion operators are given for the linear equation. The gas flows described by the fundamental polynomials of small degrees have been studied in details figures.










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