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CONTACT SYMMETRIES AND CONSERVATION LAWS FOR SOME EQUATIONS IN ISENTROPIC GAS DYNAMICS

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc 1993. Вып.3. С. 9-15.

      A sufficient point transformation condition is derived for contact symmetries within a special class of second-order quasilinear equations with three independent variables. A simple criterion is found for variational nature of symmetries for Monge-Amper equations and second- order quasilinear equations that are Euler-Lagraage equations for a variational problem. The results obtained allowed to evaluate the contact symmetries and conservation laws for equations that result from the systems describing vortex-free steady-state isentropic 3-D and 2-D unsteady plane and symmetric flows of polytropic gas. Group classification is made for these equations regarding к parameter that represents the gas adiabatic index for к > 1.










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