English

On the integrability conditions for some structures related to evolution differential equations

Differential Geometry 2007-05-23 v2 High Energy Physics - Theory Mathematical Physics Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

Abstract

Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).

Cite

@article{arxiv.math/0310451,
  title  = {On the integrability conditions for some structures related to evolution differential equations},
  author = {Paul Kersten and Iosif Krasil'shchik and Alexander Verbovetsky},
  journal= {arXiv preprint arXiv:math/0310451},
  year   = {2007}
}

Comments

5 pages, AMS-LaTeX. v2: minor corrections