부산대학교 도서관

AbstractIn this paper we employ a “direct method” to construct rank-k solutions, expressible in Riemann invariants, to hyperbolic system of first order quasilinear di!erential equations in many dimensions. The most important feature of our approach is the analysis of group invariance properties of these solutions and applying the conditional symmetry reduction technique to the initial equations. We discuss in detail the necessary and su"cient conditions for existence of these type of solutions. We demonstrate our approach through several examples of hydrodynamic type systems; new classes of solutions are obtained in a closed form.