2012/05/16 by Boris Khesin, Khesin, Boris, Fedor Soloviev +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Symplectic Geometry (math.SG) #math.DS #math.SG #nlin.SI
paper · pdf · doi:10.48550/arxiv.1205.3744
11 pages, 3 figures; This note is a short announcement of arXiv:1204.0756
arxiv created 2012/05/16 · arxiv updated 2012/05/17
We extend the definition of the pentagram map from 2D to higher dimensions and describe its integrability properties for both closed and twisted polygons by presenting its Lax form. The corresponding continuous limit of the pentagram map in dimension d is shown to be the (2,d+1)-flow of the KdV hierarchy, generalizing the Boussinesq equation in 2D.