On billiard weak solutions of nonlinear PDE's and Toda flows

Details On billiard weak solutions of nonlinear PDE's and Toda flows On billiard weak solutions of nonlinear PDE's and Toda flows

2000-05-02

arxiv.org/abs/nlin/0005006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, to be published in CRM Proc. & Lecture Notes, AMS, 25, 1--11, 2000

Scientific paper

A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives ("peakons"). The time evolution of peaks of such solutions is governed by a finite dimensional completely integrable system. Explicit solutions of this system are constructed by using algebraic-geometric method which casts it as a flow on an appropriate Riemann surface and reduces it to a classical Jacobi inversion problem. The algebraic structure of the finite dimensional flow is also examined in the context of the Toda flow hierarchy. Generalized peakon systems are obtained for any simple Lie algebra and their complete integrability is demonstrated.

Affiliated with

Also associated with

No associations

Rating

On billiard weak solutions of nonlinear PDE's and Toda flows 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 On billiard weak solutions of nonlinear PDE's and Toda flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On billiard weak solutions of nonlinear PDE's and Toda flows will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-231266