On classification of discrete, scalar-valued Poisson Brackets

Details On classification of discrete, scalar-valued Poisson Brackets On classification of discrete, scalar-valued Poisson Brackets

2011-09-20

arxiv.org/abs/1109.4327v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type transformations. Finally, improving a consolidation lattice procedure, we obtain new families of non-degenerate, vector-valued and first order dDGPBs, which can be considered in the framework of admissible Lie-Poisson group theory.

Affiliated with

Also associated with

No associations

Rating

On classification of discrete, scalar-valued Poisson Brackets 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 classification of discrete, scalar-valued Poisson Brackets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On classification of discrete, scalar-valued Poisson Brackets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-147574