New class of symmetries and exact solution to the unsteady equations of adiabatic gas dynamics

In this paper, we present a new method to obtain a new class of symmetries and invariant solution associated with the symmetries. The key point of our method is to find symmetry group of point transformations on a special solution. To demonstrate our method, we consider a spherically symmetric dynamics of an adiabatic gases, which describes a contracting and expanding localized mass of gas.