| Abstract: | In this paper, we explicitly characterize a class of solutions to the first order quasilinear system of partial differential
equations (PDEs), governing one dimensional unsteady planar and radially symmetric flows of an adiabatic gas involving shock
waves. For this, Lie group analysis is used to identify a finite number of generators that leave the given system of PDEs
invariant. Out of these generators, two commuting generators are constructed involving some arbitrary constants. With the
help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous
system, whose simple solutions provide non trivial solutions of the original system. It is interesting to remark that one
of the special solutions obtained here, using this approach, is precisely the blast wave solution known in the literature. |
