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THE BASIS OF THE POLYNOMIAL-TYPE CONTACT CONSERVATION LAWS IN ONE-DIMENSIONAL GAS DYNAMICS

V. E. Shemarulin, G. G. Farafontov
VANT. Ser. Mat. Mod. Fiz. Proc 1991. Вып.1. С. 44-50.

      The basis of the contact conservation laws of the polynomial type has been found, it describes one-dimensional plane isentropic flows a polytropic gas. It is demonstrated that any “analytical” conservation law is represented in the form of a series of the basis conservation laws, the functions generating the basis conservation laws are obtained by multiply using the recursion operator from unit, while the basis conservation laws themselves are obtained by successively using the recursion operator from the mass conservation law. As a consequence, differential relations have been obtained for special Gegenbauer polynomials. General solutions have been found to the differential equations describing these polynomials.










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