Gasdynamic wave-wave interactions. A short comparative review of some significant results

Abstract

Two distinct contexts [isentropic; strictly anisentropic] are considered for a hyperbolic quasilinear system of a gasdynamic type [Euler]. For each of these two contexts two genuinely nonlinear, geometrical, analytical and constructive approaches are considered [of a Burnat type and,  respectively, of a Martin type]. Each of these two approaches leads particularly to a pair of classes of solutions [wave solutions; wave-wave regular interaction solutions]. We finally parallel the mentioned approaches by using various comparisons between the mentioned pairs of classes. This parallel leads us to consider an ad hoc relation of continuation between the two mentioned approaches.