The conservation laws and group properties of the equations of gas dynamics with zero velocity of sound

All the conservation laws of zero order are obtained by the method of A-operators for a system of n-dimensional (n ≥ 1) equations of gas dynamics with zero velocity of sound. A group subdivision is carried out of this system with respect to an infinite subgroup, which is a normal divider of its main Lie group of transformations; the main group of the resolving system is obtained. First-order non-local symmetries are obtained for the initial system. A special choice of the mass Lagrange variables enables this system to be converted to a reduced system equivalent to it, containing n - 1 spatial variables, which, for n = 2, is written in the form of a one-dimensional complex heat-conduction equation using complex dependent and independent variables.