Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability

Details Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability

2004-12-24

arxiv.org/abs/nlin/0412064v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, Latex, to appear in Proc. Royal Soc. A. The formulation of the main result (Theorem 2) is refined and a full proof i

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-581581