EXACT-SOLUTIONS TO THE EQUATIONS OF IDEAL GAS-DYNAMICS BY MEANS OF THE SUBSTITUTION PRINCIPLE

In this paper the equations governing three-dimensional unsteady flows of an inviscid, thermally non-conducting fluid, subjected to no extra neous force, are considered. First, some simple exact solutions are ex plicitly determined; then, by using the invariance of the given equati ons with respect to, a generalized stretching group of all but space v ariables and a generalized time translation new solutions are immediat ely constructed. This invariance is known in the literature as substit ution principle, since it allows to generate new solutions (substitute d flows) from given solutions. (C) 1997 Elsevier Science Ltd.