Consider a strong explosion (such as nuclear bombs) that releases a large amount of energy  in a small volume during a short time interval. This will create a strong spherical shock wave propagating outwards from the explosion center. The self-similar solution tries to describe the flow when the shock wave has moved through a distance that is extremely large when compared to the size of the explosive. At these large distances, the information about the size and duration of the explosion will be forgotten; only the energy released  will have influence on how the shock wave evolves. To a very high degree of accuracy, then it can be assumed that the explosion occurred at a point (say the origin ) instantaneously at time .
The shock wave in the self-similar region is assumed to be still very strong such that the pressure behind the shock wave  is very large in comparison with the pressure (atmospheric pressure) in front of the shock wave , which can be neglected from the analysis. Although the pressure of the undisturbed gas is negligible, the density of the undisturbed gas  cannot be neglected since the density jump across strong shock waves is finite as a direct consequence of Rankine–Hugoniot conditions. This approximation is equivalent to setting  and the corresponding sound speed , but keeping its density non zero, i.e., .
The only parameters available at our disposal are the energy  and the undisturbed gas density . The properties behind the shock wave such as  are derivable from those in front of the shock wave. The only non-dimensional combination available from  and  is
It is reasonable to assume that the evolution in  and  of the shock wave depends only on the above variable. This means that the shock wave location  itself will correspond to a particular value, say , of this variable, i.e.,
The propagation velocity of the shock wave is
With the approximation described above, Rankine–Hugoniot conditions determines the gas velocity immediately behind the shock front ,  and  for an ideal gas as follows
where  is the specific heat ratio. Since  is a constant, the density immediately behind the shock wave is not changing with time, whereas  and  decrease as  and , respectively.