SOME INTEGRABILITY CASES OF FACTOR-EQUATIONS FOR POLYTROPIC GAS 1-D DYNAMICS

O.I. Morozov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.2. С. 55-65.

      The paper studies cases of integrability in factor-equation quadratures relevant to 1-D subalgebra optimum system of symmetry algebra for polytropic gas 1-D dynamics in Lagrangian equations.
      The factor-equations are reduced to Abelian equations, for which cases of reducibility to linear and Bernoulli equations are studied. This allows to find new analytical solutions of gas dynamics equations.