TY - JOUR
T1 - Rank-κ solutions of hydrodynamic-type systems
AU - Grundland, A. M.
AU - Huard, B.
N1 - Funding Information:
This work was supported in part by the NSERC of Canada and the FQRNT.
PY - 2007/7/1
Y1 - 2007/7/1
N2 - We present a variant of the conditional symmetry method for obtaining rank-k solutions in terms of Riemann invariants for first-order quasilinear hyperbolic systems of PDEs in many dimensions and discuss examples of applying the proposed approach to fluid dynamics equations in n+1 dimensions in detail. We obtain several new types of algebraic, rational, and soliton-like solutions (including kinks, bumps, and multiple-wave solutions).
AB - We present a variant of the conditional symmetry method for obtaining rank-k solutions in terms of Riemann invariants for first-order quasilinear hyperbolic systems of PDEs in many dimensions and discuss examples of applying the proposed approach to fluid dynamics equations in n+1 dimensions in detail. We obtain several new types of algebraic, rational, and soliton-like solutions (including kinks, bumps, and multiple-wave solutions).
KW - Conditional symmetry
KW - Rank-k solution of partial differential equations
KW - Riemann invariant
UR - http://www.scopus.com/inward/record.url?scp=34548387980&partnerID=8YFLogxK
U2 - 10.1007/s11232-007-0080-6
DO - 10.1007/s11232-007-0080-6
M3 - Article
AN - SCOPUS:34548387980
VL - 152
SP - 948
EP - 962
JO - Journal of Physics A: Mathematical Nuclear and General
JF - Journal of Physics A: Mathematical Nuclear and General
SN - 1751-8113
IS - 1
ER -