TY - JOUR
T1 - Riemann Invariants and Rank-k Solutions of Hyperbolic Systems
AU - Grundland, A. Michel
AU - Huard, Benoit
PY - 2006
Y1 - 2006
N2 - In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the necessary and sufficient conditions for existence of these type of solutions written in terms of Riemann invariants. The most important characteristic of this approach is the introduction of specific first order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method of solving multi-dimensional systems of PDEs. We have demonstrated the usefulness of our approach through several examples of hydrodynamic type systems; new classes of solutions have been obtained in a closed form.
AB - In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the necessary and sufficient conditions for existence of these type of solutions written in terms of Riemann invariants. The most important characteristic of this approach is the introduction of specific first order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method of solving multi-dimensional systems of PDEs. We have demonstrated the usefulness of our approach through several examples of hydrodynamic type systems; new classes of solutions have been obtained in a closed form.
UR - http://www.tandfonline.com/doi/abs/10.2991/jnmp.2006.13.3.6
U2 - 10.2991/jnmp.2006.13.3.6
DO - 10.2991/jnmp.2006.13.3.6
M3 - Article
SN - 1402-9251
VL - 13
SP - 393
EP - 419
JO - Journal of Nonlinear Mathematical Physics
JF - Journal of Nonlinear Mathematical Physics
IS - 3
ER -