Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
| dc.creator | Ferapontov, E. V. | |
| dc.creator | Khusnutdinova, K. R. | |
| dc.date | 2004-12-24 | |
| dc.date | 2005-11-29 | |
| dc.date.accessioned | 2026-07-07T06:40:17Z | |
| dc.date.available | 2026-07-07T06:40:17Z | |
| dc.description | An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existence of special solutions known as `double waves' is equivalent to the diagonalizability of an arbitrary matrix of the two-parameter family (kE+A)^{-1}(lE+B). Since the diagonalizability can be effectively verified by differential-geometric means, this provides a simple necessary condition for integrability. | |
| dc.description | 27 pages, Latex, to appear in Proc. Royal Soc. A. The formulation of the main result (Theorem 2) is refined and a full proof is given | |
| dc.identifier | https://arxiv.org/abs/nlin/0412064 | |
| dc.identifier | http://arxiv.org/abs/nlin/0412064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101356 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability | |
| dc.type | text |