English

Exact Poisson pencils, $\tau$-structures and topological hierarchies

Exactly Solvable and Integrable Systems 2011-12-23 v2 Mathematical Physics math.MP

Abstract

We discuss, in the framework of Dubrovin-Zhang's perturbative approach to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of Poisson pencils, called exact Poisson pencils. In particular we show that, in the semisimple case, exactness of the pencil is equivalent to the constancy of the so-called "central invariants" of the theory that were introduced by Dubrovin, Liu and Zhang.

Keywords

Cite

@article{arxiv.1106.1546,
  title  = {Exact Poisson pencils, $\tau$-structures and topological hierarchies},
  author = {Gregorio Falqui and Paolo Lorenzoni},
  journal= {arXiv preprint arXiv:1106.1546},
  year   = {2011}
}

Comments

31 pages, final version to appear in Physica D: Nonlinear Phenomena