Volume 13, Issue 3, August 2006, Pages 393 - 419
Riemann Invariants and Rank-k Solutions of Hyperbolic Systems
- A.M. GRUNDLAND 0, B. HUARD 1
- Corresponding Author
- A.M. GRUNDLAND
0Centre de Recherches Mathématiques, Université de Montréal
1Centre de Recherches Mathématiques, Université de Montréal
Available Online 1 August 2006.
- https://doi.org/10.2991/jnmp.2006.13.3.6How to use a DOI?
- Riemann invariants, Rank-k Solutions, quasilinear differential equations
- In this paper we employ a “direct method” to construct rank-k solutions, express- ible in Riemann invariants, to hyperbolic system of first order quasilinear differential 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 neces- sary and sufficient 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
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- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - A.M. GRUNDLAND AU - B. HUARD PY - 2006 DA - 2006/08 TI - Riemann Invariants and Rank-k Solutions of Hyperbolic Systems JO - Journal of Nonlinear Mathematical Physics SP - 393 EP - 419 VL - 13 IS - 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.3.6 DO - https://doi.org/10.2991/jnmp.2006.13.3.6 ID - GRUNDLAND2006 ER -