Exact Poisson pencils, $τ$-structures and topological hierarchies

Details Exact Poisson pencils, $τ$-structures and topological hierarchies Exact Poisson pencils, $τ$-structures and topological hierarchies

2011-06-08

arxiv.org/abs/1106.1546v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1016/j.physd.2011.11.009

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.

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