Journal of Nonlinear Mathematical Physics

Volume 13, Issue 3, August 2006, Pages 393 - 419

Riemann Invariants and Rank-k Solutions of Hyperbolic Systems

Authors
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.
DOI
https://doi.org/10.2991/jnmp.2006.13.3.6How to use a DOI?
Keywords
Riemann invariants, Rank-k Solutions, quasilinear differential equations
Abstract
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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 3
Pages
393 - 419
Publication Date
2006/08
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2006.13.3.6How to use a DOI?
Open Access
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  -