Inheritance of Generic Singularities of Solutions of a Linear Wave Equation by Solutions of Isoentropic Gas Motion Equations

It is shown that the catastrophe germs of smooth mappings determining the three generic (in the sense of mathematical catastrophe theory) singularities of solutions of systems of equations for a one-dimensional isoentropic gas coincide with the germs corresponding to similar singularities of solutions of a linear wave equation with constant coefficients. The conjecture is put forth that such an inheritance for generic singularities of solutions of systems of equations for a isoentropic gas must also take place in spatially multidimensional cases.