English

Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy

solv-int 2009-10-31 v1 Exactly Solvable and Integrable Systems

Abstract

We use ideas of the geometry of bihamiltonian manifolds, developed by Gel'fand and Zakharevich, to study the KP equations. In this approach they have the form of local conservation laws, and can be traded for a system of ordinary differential equations of Riccati type, which we call the Central System. We show that the latter can be linearized by means of a Darboux covering, and we use this procedure as an alternative technique to construct rational solutions of the KP equations.

Keywords

Cite

@article{arxiv.solv-int/9806002,
  title  = {Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy},
  author = {Gregorio Falqui and Franco Magri and Marco Pedroni},
  journal= {arXiv preprint arXiv:solv-int/9806002},
  year   = {2009}
}

Comments

Latex, 27 pages. To appear in Commun. Math. Phys