Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
Exactly Solvable and Integrable Systems
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.nlin/0412064,
title = {Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability},
author = {E. V. Ferapontov and K. R. Khusnutdinova},
journal= {arXiv preprint arXiv:nlin/0412064},
year = {2007}
}
Comments
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