Completely integrable curve flows on Adjoint orbits

Details Completely integrable curve flows on Adjoint orbits Completely integrable curve flows on Adjoint orbits

2001-08-22

arxiv.org/abs/math/0108154v1

Mathematics

Differential Geometry

25 pages

Scientific paper

It is known that the Schr\"odinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schr\"odinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the $n$-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on Adjoint $U$-orbits from flows in the soliton hierarchy associated to a compact Lie group $U$. There are natural geometric bi-Hamiltonian structures on the space of curves on Adjoint orbits, and they correspond to the order two and three Hamiltonian structures on soliton equations under our construction. We study the Hamiltonian theory of these geometric curve flows and also give several explicit examples.

Affiliated with

Also associated with

No associations

Rating

Completely integrable curve flows on Adjoint orbits 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 Completely integrable curve flows on Adjoint orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completely integrable curve flows on Adjoint orbits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190095